Papers by Fabrizio Canfora
arXiv (Cornell University), Dec 28, 2018
We construct an analytic black hole solution in SU (2) Einstein-Yang-Mills theory in five dimensi... more We construct an analytic black hole solution in SU (2) Einstein-Yang-Mills theory in five dimensions supporting a Meron field. The gauge field is proportional to a pure gauge and has a non-trivial topological charge. The would-be singularity at the Meron core gets shielded from the exterior by the black hole horizon. The metric has only one integration constant, namely, its ADM mass, which is shown to be finite once an appropriate boundary term is added to the action. The thermodynamics is also worked out, and a first-order phase transition, similar to the one occurring in the Reissner-Nordström case is identified. We also show that the solution produces a spin from isospin effect, i.e., even though the theory is constructed out of bosons only, the combined system of a scalar field and this background may become fermionic. More specifically, we study scalar excitations in this purely bosonic background and find that the system describes fermionic degrees of freedom at spatial infinity. Finally, for the asymptotically AdS 5 case, we study its consequences in the context of the AdS/CFT correspondence.
Nuclear Physics B, Dec 1, 2005
A Large N expansion for gravity is proposed. The scheme is based on the splitting of the Einstein... more A Large N expansion for gravity is proposed. The scheme is based on the splitting of the Einstein-Hilbert action into the BF topological action plus a constraint. The method also allows to include matter fields. The relation between matter and non orientable fat graphs in the expansion is stressed; the special role of scalars is shortly discussed. The connections with the Holographic Principle and higher spin fields are analyzed.
arXiv (Cornell University), Jun 5, 2017
By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimension... more By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimensional Skyrme model, the generalized hedgehog and the rational map ansatz, we find multi-Skyrmion configurations in AdS 2 × S 2. We construct Skyrmionic multi-layered configurations such that the total Baryon charge is the product of the number of kinks along the radial AdS 2 direction and the degree of the rational map. We show that, for fixed total Baryon charge, as one increases the charge density on ∂ (AdS 2 × S 2), it becomes increasingly convenient energetically to have configurations with more peaks in the radial AdS 2 direction but a lower degree of the rational map. This has a direct relation with the so-called holographic popcorn transitions in which, when the charge density is high, multi-layered configurations with low charge on each layer are favored over configurations with few layers but with higher charge on each layer. The case in which the geometry is M 2 × S 2 can also be analyzed.
arXiv (Cornell University), Jul 5, 2018
A consistent ansatz for the Skyrme model in (3+1)-dimensions which is able to reduce the complete... more A consistent ansatz for the Skyrme model in (3+1)-dimensions which is able to reduce the complete set of Skyrme field equations to just one equation for the profile in situations in which the Baryon charge can be arbitrary large is introduced: moreover, the field equation for the profile can be solved explicitly. Such configurations describe ordered arrays of Baryonic tubes living in flat space-times at finite density. The plots of the energy density (as well as of the Baryon density) clearly show that the regions of maximal energy density have the shape of a tube: the energy density and the Baryon density depend periodically on two spatial directions while they are constant in the third spatial direction. Thus, these topologically non-trivial crystal-like solutions can be intepreted as configurations in which most of the energy density and the baryon density are concentrated within tube-shaped regions. The positions of the energy-density peaks can be computed explicitly and they manifest a clear crystalline order. A non-trivial stability test is discussed.
Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra... more Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of a sub-class of these gravitational fields have wave-like character. It is shown that they have spin 1. Indirect observational effects of spin 1 gravitational waves will be discussed. In particular, the emission of spin 1 gravitational waves from binary systems is considered. In cosmology, it is shown that vector perturbations are not anymore negligible in the presence of topological defects and this could be verified by looking at the CMB anisotropies.
Physical Review D, Apr 23, 2015
We extend the investigation of BPS saturated t'Hooft-Polyakov monopoles in M 2 × S 2 to the gener... more We extend the investigation of BPS saturated t'Hooft-Polyakov monopoles in M 2 × S 2 to the general case of SU (N) gauge symmetry. This geometry causes the resulting N − 1 coupled nonlinear ordinary differential equations for the N − 1 monopole profiles to become autonomous. One can also define a flat limit in which the curvature of the background metric is arbitrarily small but the simplifications brought in by the geometry remain. We prove analytically that non-trivial solutions in which the profiles are not proportional can be found. Moreover, we construct numerical solutions for N = 2, 3 and 4. The presence of the parameter N allows one to take a smooth large N limit which greatly simplifies the treatment of the infinite number of profile function equations. We show that, in this limit, the system of infinitely many coupled ordinary differential equations for the monopole profiles reduces to a single two-dimensional non-linear partial differential equation.
Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018), 2019
We consider finite-temperature SU(2) gauge theory in the continuum formulation. Choosing the Land... more We consider finite-temperature SU(2) gauge theory in the continuum formulation. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy with respect to the Polyakov-loop parameter and solving the Gribov gap equation. The main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. Finally, problems for the pressure at low temperatures are reported.
Physical Review D, 2017
We construct the first analytic examples of topologically non-trivial solutions of the (3+1)dimen... more We construct the first analytic examples of topologically non-trivial solutions of the (3+1)dimensional U (1) gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the U (1) gauged Skyrme model whose periodic time-dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contribute directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.
Physical Review D, 2016
It is analyzed the quantum mechanical scattering off a topological defect (such as a Dirac monopo... more It is analyzed the quantum mechanical scattering off a topological defect (such as a Dirac monopole) as well as a Yukawa-like potential(s) representing the typical effects of strong interactions. This system, due to the presence of a short-range potential, can be analyzed using the powerful technique of the complex angular momenta which, so far, has not been employed in the presence of monopoles (nor of other topological solitons). Due to the fact that spatial spherical symmetry is achieved only up to internal rotations, the partial wave expansion becomes very similar to the Jacob-Wick helicity amplitudes for particles with spin. However, since the angular-momentum operator has an extra "internal" contribution, fixed cuts in the complex angular momentum plane appear. Correspondingly, the background integral in the Regge formula does not decrease for large values of |cos θ| (namely, large values of the Mandelstam variable s). Hence, the experimental observation of this kind of behavior could be a direct signal of non-trivial topological structures in strong interactions. The possible relations of these results with the soft Pomeron are shortly analyzed.
Physics Letters B, 2016
The Gribov problem in the presence of a background field is analyzed: in particular, we study the... more The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.
Physics Letters B, 2017
Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon mod... more Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions-anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions-anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.
Nuclear Physics B, 2017
By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimension... more By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimensional Skyrme model, the generalized hedgehog and the rational map ansatz, we find multi-Skyrmion configurations in AdS 2 × S 2. We construct Skyrmionic multi-layered configurations such that the total Baryon charge is the product of the number of kinks along the radial AdS 2 direction and the degree of the rational map. We show that, for fixed total Baryon charge, as one increases the charge density on ∂ (AdS 2 × S 2), it becomes increasingly convenient energetically to have configurations with more peaks in the radial AdS 2 direction but a lower degree of the rational map. This has a direct relation with the so-called holographic popcorn transitions in which, when the charge density is high, multi-layered configurations with low charge on each layer are favored over configurations with few layers but with higher charge on each layer. The case in which the geometry is M 2 × S 2 can also be analyzed.
Nuclear Physics B, 2016
In this paper we analyze the interactions of a massive spin-2 particles charged under both Abelia... more In this paper we analyze the interactions of a massive spin-2 particles charged under both Abelian and non-Abelian group using the Porrati-Rahman Lagrangian. This theory is valid up to an intrinsic cutoff scale. Phenomenologically a theory valid up to a cutoff scale is sensible as all known higher spin particles are non-fundamental and it is shown that indeed this action can be used to estimate some relevant cross section. Such action necessarily includes St .. uckelberg field and therefore it is necessary to fix the corresponding gauge symmetry. We show that this theory, when the St .. uckelberg symmetry is gauge-fixed, possesses a non-trivial infrared problem. A gauge fixing ambiguity arises which is akin to the Gribov problem in QCD in the Abelian case as well. In some cases (such as when the space-time is the four-dimensional torus) the vacuum copies can be found analytically. A similar phenomenon also appears in the case of Proca fields. A very interesting feature of these copies is that they arise only for "large enough" gauge potentials. This opens the possibility to avoid the appearance of such gauge fixing ambiguities by using a Gribov-Zwanziger like approach.
The European Physical Journal C, 2016
In this paper the compatibility is analyzed of the non-perturbative equations of state of quarks ... more In this paper the compatibility is analyzed of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for selfgravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier's principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the latest lattice data. In the quark case, there is a small but non-vanishing range of temperatures in which it is not possible to define a single-valued functional relation between density and pressure. Interestingly enough, a small change of the parameters appearing in the fit of the lattice quark propagator (of around 10 %) could guarantee the fulfillment of all the three conditions (keeping alive, at the same time, the violation of positivity of the spectral representation, which is the expected signal of confinement). As far as gluons are concerned, the analysis shows very similar results. Whether or not the non-perturbative quark and gluon propagators satisfy these conditions can have a strong impact on the estimate of the maximal mass of quark stars.
Journal of High Energy Physics, 2016
It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncom... more It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.
The European Physical Journal C, 2015
We study multi-soliton solutions of the fourdimensional SU(N) Skyrme model by combining the hedge... more We study multi-soliton solutions of the fourdimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of S 2 into C P N −1 and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric setup allows to introduce a parameter which is related to the 't Hooft coupling of a suitable large N limit, in which N → ∞ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it.
Journal of High Energy Physics, 2014
We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field w... more We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat and, moreover, allows one to use analytical tools which in the flat case are not available. Some of the analytic configurations, in the limit of vanishing Higgs coupling, correspond to magnetic monopoles and dyons living within this tube-shaped domain. However, unlike what happens in the standard case, analytical solutions can also be found in the case in which the Higgs coupling is non-vanishing. We further show that the system admits long-lived breathers.
Physical Review D, 2014
Exact analytic solutions of the Skyrme model defined on a spherically symmetric R (1,1) × S 2 geo... more Exact analytic solutions of the Skyrme model defined on a spherically symmetric R (1,1) × S 2 geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the compression modulus are found in good agreement with experiments by fitting the masses MN and M∆.
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Papers by Fabrizio Canfora