We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalie... more We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalies present in Weyl-invariant and diffeomorphism-invariant effective actions for two dimensional massless scalar fields in a gravitational background. We find that the Schwinger terms are not sensitive to the regularization procedure and that they are independent of the background metric.
The canonical quantization method for collective coordinates in crystalline configurations of the... more The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the binding energy resulting from the isospin degrees of freedom. This leads to a consistent description of asymmetric nuclear matter within the Skyrme framework and allows us to compute the symmetry energy of the Skyrmionic crystal as a function of the baryon density, and to compare with recent observational constraints. CONTENTS I. Introduction 1 II. Generalized Skyrme model and classical crystals 2 A. The model 2 B. The classical crystal of Skyrmions 3 C. The Skyrme crystal EoS for symmetric nuclear matter 3 III. Quantization of the Skyrme crystal 4 A. The internal symmetry of Skyrme crystals and the isospin group 4 B. Quantum isospin states and Hilbert space 5 C. Isospin correction to the energy per baryon 7 IV. Quantum skyrmion crystals and the symmetry energy of npe(µ) matter 9 A. The electric charge density of pure Skyrmion matter 10 B. The symmetry energy 10 C. Particle fractions of npeµ matter in β-equilibrium 12 V. Conclusions 13 Acknowledgments 13 A. Calculation of matrix elements 13 B. Isospin inertia tensor of Skyrme crystals 14 References 15
In some recent papers it is claimed that the physical significance of the vacuum angle theta for ... more In some recent papers it is claimed that the physical significance of the vacuum angle theta for QCD-like theories depends on the chosen gauge condition. We criticise the arguments that were given in support of this claim, and show by explicit construction for the case of QED 2 that and why they fail, confirming thereby the commonly accepted point of view.
This paper addresses the prediction of the median peak floor acceleration (PFA) demand of elastic... more This paper addresses the prediction of the median peak floor acceleration (PFA) demand of elastic structures subjected to seismic excitation by means of an adapted response spectrum method. Modal combination is based on a complete quadratic combination (CQC) rule. In contrast to previous studies, in the present contribution closed form solutions for the correlation coefficients and peak factors entering the CQC rule are derived using concepts of normal stationary random vibration theory. A ground motion set, which matches the design response spectrum for a specific site and a target dispersion, is used to define the stochastic base excitation. The response spectrum method is tested for various planar and spatial generic high-rise structures subjected to this particular ground motion set. A comparison of the outcomes with the results of computationally more expensive response history analyses shows the applicability and accuracy of the proposed simplified method.
Boson stars represent a hypothetical exotic type of compact stellar object that may be observed f... more Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future GW detectors. In this work we show that the moment of inertia I, the (dimensionless) angular momentum χ and the quadrupole moment Q of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained I − χ − Q relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e. model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars.
We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from... more We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry-accounting for the proton-neutron mass difference-to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclear and low-energy strong interaction physics.
We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimens... more We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimensions. We find that the existence of a certain class of zero modes is related to a specific topological property precisely when the requirement of finite Chern-Simons action is imposed. In addition we find that we also have a solution to the three dimensional Seiberg-Witten equations. This requires automatically the inclusion of a Chern-Simons term in the action and consequent connections with a topological mass for the gauge field.
We propose a new equation of state for nuclear matter based on a generalized Skyrme model which i... more We propose a new equation of state for nuclear matter based on a generalized Skyrme model which is consistent with all current constraints on the observed properties of neutron stars. This generalized model depends only on two free parameters related to the ranges of pressure values at which different submodels are dominant, and which can be adjusted so that mass-radius and deformability constraints from astrophysical and gravitational wave measurements can be met. Our results support the Skyrme model and its generalizations as good candidates for a low energy effective field-theoretic description of nuclear matter even at extreme conditions such as those inside neutron stars.
We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are mul... more We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number (or topological charge) B = ±1 but not for higher |B|. This implies that higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model. We provide a simple and explicit example for this possibility. Further, we show that the |B| = 1 BPS sector continues to exist for certain generalizations of the model like, for instance, after its coupling to a specific version of the BPS Skyrme model, i.e., the addition of the sextic term and a particular potential.
The full-text may be used and/or reproduced, and given to third parties in any format or medium, ... more The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.
Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtaine... more Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable. Further, we compare both exact and mean-field results with some theoretical and phenomenological constraints on neutron star properties, demonstrating thus the relevance of our model even in its most simple version.
We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particula... more We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density-their thermodynamical functions as well as the equation of state agree in this limit. This fact allows to read off some properties of the ω-meson from the BPS Skyrme action, even though the latter model is entirely based on the (pionic) SU (2) Skyrme field. On the other hand, at low densities, at the order of the usual nuclear matter density, the equations of state of the two models are no longer universal, such that a comparison depends on some model details. Still, also the BPS Skyrme model gives rise to nuclear saturation in this regime, leading, in fact, to an exact balance between repulsive and attractive forces. The perfect fluid aspects of the BPS Skyrme model, which, together with its BPS properties, form the base of our results, are shown to be in close formal analogy with the Eulerian formulation of relativistic fluid dynamics. Within this analogy, the BPS Skyrme model, in general, corresponds to a non-barotropic perfect fluid.
Recently, within the space of generalized Skyrme models, a BPS submodel was identified which repr... more Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is exp...
We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for ph... more We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a ferromagnetic liquid. Such a transition can be generated by increasing the external pressure P or by turning on an external magnetic field H. As a consequence, the topological phase where gauged BPS baby skyrmions exist, is a higher density phase. For smaller densities, obtained for smaller values of P and H, a phase without solitons is reached. We find the critical line in the P, H parameter space. Furthermore, in the soliton phase, we find the equation of state for the baby skyrmion matter V = V (P, H) at zero temperature, where V is the "volume", i.e., area of the solitons.
We derive a systematic procedure of computing the vacuum functional and fermion condensate of the... more We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.
The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consi... more The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consisting of the standard sigma model and the Skyrme terms, a potential, and a certain term sextic in first derivatives. Here we demonstrate that, in this theory, each pair of terms in the static energy functional which may support topological solitons according to the Derrick criterion (i.e., each pair of terms with opposite Derrick scaling) separately posesses a topological energy bound. As a consequence, there exists a four-parameter family of topological bounds for the full generalized Skyrme model. The optimal bounds, i.e., the optimal values of the parameters, depend both on the form of the potential and on the relative strength of the different terms. It also follows that various submodels of the generalized Skyrme model have one-parameter families of topological energy bounds. We also consider the case of topological bounds for the generalized Skyrme model on a compact base space as well as generalizations to higher dimensions.
The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model a... more The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field H and under external pressure P , i.e., V = V (P, H), where V is the "volume" (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium.
One problem in the application of the Skyrme model to nuclear physics is that it predicts too lar... more One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of the BPS Skyrme model at zero temperature and calculate its equation of state. Among other results, we find that classically (i.e. without taking into account quantum corrections) the compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero compression modulus. This suggests that the inclusion of the BPS submodel into the Skyrme model lagrangian may significantly reduce this too large value, providing further evidence for the claim that the BPS Skyrme model may play an important role in the description of nuclei and nuclear matter.
If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS ... more If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related BPS equations. We point out that this fact may be understood as a simple consequence of an appropriately generalised notion of self-duality. We show that this self-duality framework enables us to generalize to higher dimensions the construction of new solitons from already known solutions. By performing simple field transformations our procedure allows us to relate solitons with different topological properties. We present several interesting examples of such solitons in two and three dimensions.
We continue the investigation of supersymmetric extensions of baby Skyrme models in d = 2 + 1 dim... more We continue the investigation of supersymmetric extensions of baby Skyrme models in d = 2 + 1 dimensions. In a first step, we show that the CP(1) form of the baby Skyrme model allows for the same N = 1 SUSY extension as its O(3) formulation. Then we construct the N = 1 SUSY extension of the gauged baby Skyrme model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a next step, we investigate the issue of N = 2 SUSY extensions of baby Skyrme models. We find that all gauged and ungauged submodels of the baby Skyrme model which support BPS soliton solutions allow for an N = 2 extension such that the BPS solutions are one-half BPS states (i.e., annihilated by one-half of the SUSY charges). In the course of our investigation, we also derive the general BPS equations for completely general N = 2 supersymmetric field theories of (both gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear sigma model as a further, concrete example.
We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalie... more We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalies present in Weyl-invariant and diffeomorphism-invariant effective actions for two dimensional massless scalar fields in a gravitational background. We find that the Schwinger terms are not sensitive to the regularization procedure and that they are independent of the background metric.
The canonical quantization method for collective coordinates in crystalline configurations of the... more The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the binding energy resulting from the isospin degrees of freedom. This leads to a consistent description of asymmetric nuclear matter within the Skyrme framework and allows us to compute the symmetry energy of the Skyrmionic crystal as a function of the baryon density, and to compare with recent observational constraints. CONTENTS I. Introduction 1 II. Generalized Skyrme model and classical crystals 2 A. The model 2 B. The classical crystal of Skyrmions 3 C. The Skyrme crystal EoS for symmetric nuclear matter 3 III. Quantization of the Skyrme crystal 4 A. The internal symmetry of Skyrme crystals and the isospin group 4 B. Quantum isospin states and Hilbert space 5 C. Isospin correction to the energy per baryon 7 IV. Quantum skyrmion crystals and the symmetry energy of npe(µ) matter 9 A. The electric charge density of pure Skyrmion matter 10 B. The symmetry energy 10 C. Particle fractions of npeµ matter in β-equilibrium 12 V. Conclusions 13 Acknowledgments 13 A. Calculation of matrix elements 13 B. Isospin inertia tensor of Skyrme crystals 14 References 15
In some recent papers it is claimed that the physical significance of the vacuum angle theta for ... more In some recent papers it is claimed that the physical significance of the vacuum angle theta for QCD-like theories depends on the chosen gauge condition. We criticise the arguments that were given in support of this claim, and show by explicit construction for the case of QED 2 that and why they fail, confirming thereby the commonly accepted point of view.
This paper addresses the prediction of the median peak floor acceleration (PFA) demand of elastic... more This paper addresses the prediction of the median peak floor acceleration (PFA) demand of elastic structures subjected to seismic excitation by means of an adapted response spectrum method. Modal combination is based on a complete quadratic combination (CQC) rule. In contrast to previous studies, in the present contribution closed form solutions for the correlation coefficients and peak factors entering the CQC rule are derived using concepts of normal stationary random vibration theory. A ground motion set, which matches the design response spectrum for a specific site and a target dispersion, is used to define the stochastic base excitation. The response spectrum method is tested for various planar and spatial generic high-rise structures subjected to this particular ground motion set. A comparison of the outcomes with the results of computationally more expensive response history analyses shows the applicability and accuracy of the proposed simplified method.
Boson stars represent a hypothetical exotic type of compact stellar object that may be observed f... more Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future GW detectors. In this work we show that the moment of inertia I, the (dimensionless) angular momentum χ and the quadrupole moment Q of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained I − χ − Q relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e. model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars.
We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from... more We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry-accounting for the proton-neutron mass difference-to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclear and low-energy strong interaction physics.
We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimens... more We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimensions. We find that the existence of a certain class of zero modes is related to a specific topological property precisely when the requirement of finite Chern-Simons action is imposed. In addition we find that we also have a solution to the three dimensional Seiberg-Witten equations. This requires automatically the inclusion of a Chern-Simons term in the action and consequent connections with a topological mass for the gauge field.
We propose a new equation of state for nuclear matter based on a generalized Skyrme model which i... more We propose a new equation of state for nuclear matter based on a generalized Skyrme model which is consistent with all current constraints on the observed properties of neutron stars. This generalized model depends only on two free parameters related to the ranges of pressure values at which different submodels are dominant, and which can be adjusted so that mass-radius and deformability constraints from astrophysical and gravitational wave measurements can be met. Our results support the Skyrme model and its generalizations as good candidates for a low energy effective field-theoretic description of nuclear matter even at extreme conditions such as those inside neutron stars.
We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are mul... more We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number (or topological charge) B = ±1 but not for higher |B|. This implies that higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model. We provide a simple and explicit example for this possibility. Further, we show that the |B| = 1 BPS sector continues to exist for certain generalizations of the model like, for instance, after its coupling to a specific version of the BPS Skyrme model, i.e., the addition of the sextic term and a particular potential.
The full-text may be used and/or reproduced, and given to third parties in any format or medium, ... more The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.
Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtaine... more Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable. Further, we compare both exact and mean-field results with some theoretical and phenomenological constraints on neutron star properties, demonstrating thus the relevance of our model even in its most simple version.
We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particula... more We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density-their thermodynamical functions as well as the equation of state agree in this limit. This fact allows to read off some properties of the ω-meson from the BPS Skyrme action, even though the latter model is entirely based on the (pionic) SU (2) Skyrme field. On the other hand, at low densities, at the order of the usual nuclear matter density, the equations of state of the two models are no longer universal, such that a comparison depends on some model details. Still, also the BPS Skyrme model gives rise to nuclear saturation in this regime, leading, in fact, to an exact balance between repulsive and attractive forces. The perfect fluid aspects of the BPS Skyrme model, which, together with its BPS properties, form the base of our results, are shown to be in close formal analogy with the Eulerian formulation of relativistic fluid dynamics. Within this analogy, the BPS Skyrme model, in general, corresponds to a non-barotropic perfect fluid.
Recently, within the space of generalized Skyrme models, a BPS submodel was identified which repr... more Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is exp...
We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for ph... more We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a ferromagnetic liquid. Such a transition can be generated by increasing the external pressure P or by turning on an external magnetic field H. As a consequence, the topological phase where gauged BPS baby skyrmions exist, is a higher density phase. For smaller densities, obtained for smaller values of P and H, a phase without solitons is reached. We find the critical line in the P, H parameter space. Furthermore, in the soliton phase, we find the equation of state for the baby skyrmion matter V = V (P, H) at zero temperature, where V is the "volume", i.e., area of the solitons.
We derive a systematic procedure of computing the vacuum functional and fermion condensate of the... more We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.
The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consi... more The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consisting of the standard sigma model and the Skyrme terms, a potential, and a certain term sextic in first derivatives. Here we demonstrate that, in this theory, each pair of terms in the static energy functional which may support topological solitons according to the Derrick criterion (i.e., each pair of terms with opposite Derrick scaling) separately posesses a topological energy bound. As a consequence, there exists a four-parameter family of topological bounds for the full generalized Skyrme model. The optimal bounds, i.e., the optimal values of the parameters, depend both on the form of the potential and on the relative strength of the different terms. It also follows that various submodels of the generalized Skyrme model have one-parameter families of topological energy bounds. We also consider the case of topological bounds for the generalized Skyrme model on a compact base space as well as generalizations to higher dimensions.
The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model a... more The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field H and under external pressure P , i.e., V = V (P, H), where V is the "volume" (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium.
One problem in the application of the Skyrme model to nuclear physics is that it predicts too lar... more One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of the BPS Skyrme model at zero temperature and calculate its equation of state. Among other results, we find that classically (i.e. without taking into account quantum corrections) the compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero compression modulus. This suggests that the inclusion of the BPS submodel into the Skyrme model lagrangian may significantly reduce this too large value, providing further evidence for the claim that the BPS Skyrme model may play an important role in the description of nuclei and nuclear matter.
If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS ... more If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related BPS equations. We point out that this fact may be understood as a simple consequence of an appropriately generalised notion of self-duality. We show that this self-duality framework enables us to generalize to higher dimensions the construction of new solitons from already known solutions. By performing simple field transformations our procedure allows us to relate solitons with different topological properties. We present several interesting examples of such solitons in two and three dimensions.
We continue the investigation of supersymmetric extensions of baby Skyrme models in d = 2 + 1 dim... more We continue the investigation of supersymmetric extensions of baby Skyrme models in d = 2 + 1 dimensions. In a first step, we show that the CP(1) form of the baby Skyrme model allows for the same N = 1 SUSY extension as its O(3) formulation. Then we construct the N = 1 SUSY extension of the gauged baby Skyrme model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a next step, we investigate the issue of N = 2 SUSY extensions of baby Skyrme models. We find that all gauged and ungauged submodels of the baby Skyrme model which support BPS soliton solutions allow for an N = 2 extension such that the BPS solutions are one-half BPS states (i.e., annihilated by one-half of the SUSY charges). In the course of our investigation, we also derive the general BPS equations for completely general N = 2 supersymmetric field theories of (both gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear sigma model as a further, concrete example.
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Papers by Christoph Adam