Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of... more Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through Kähler-Atiyah bundles, which we developed in previous work. Applying this to the most general N = 2 flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.
We investigate the most general warped compactification of eleven-dimensional supergravity on eig... more We investigate the most general warped compactification of eleven-dimensional supergravity on eight-dimensional manifolds to AdS 3 spaces (in the presence of non-vanishing four-form flux) which preserves N = 2 supersymmetry in three dimensions. Without imposing any restrictions on the chirality of the internal part of the supersymmetry generators, we use geometric algebra techniques to study some implications of the supersymmetry constraints. In particular, we discuss the Lie bracket of certain vector fields constructed as pinor bilinears on the compactification manifold.
Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of... more Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through Kähler-Atiyah bundles, which we developed in previous work. Applying this to the most general N = 2 flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.
We show how supersymmetry conditions for flux compactifications of supergravity and string theory... more We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kähler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory compactifications on eight-manifolds down to AdS 3 spaces which preserve N = 2 supersymmetry in 3 dimensions. We also give a brief sketch of the lift of such equations to the cone over the compactification space and of the geometric algebra approach to 'constrained generalized Killing pinors', which forms the technical and conceptual core of our investigation.
We use the theory of singular foliations to study N = 1 compactifications of elevendimensional su... more We use the theory of singular foliations to study N = 1 compactifications of elevendimensional supergravity on eight-manifolds M down to AdS 3 spaces, allowing for the possibility that the internal part ξ of the supersymmetry generator is chiral on some locus W which does not coincide with M. We show that the complement M \ W must be a dense open subset of M and that M admits a singular foliationF endowed with a longitudinal G 2 structure and defined by a closed one-form ω, whose geometry is determined by the supersymmetry conditions. The singular leaves are those leaves which meet W. When ω is a Morse form, the chiral locus is a finite set of points, consisting of isolated zero-dimensional leaves and of conical singularities of seven-dimensional leaves. In that case, we describe the topology ofF using results from Novikov theory. We also show how this description fits in with previous formulas which were extracted by exploiting the Spin(7) ± structures which exist on the complement of W. Contents 1 Basics 2 Parameterizing a Majorana spinor on M 2.1 Globally valid parameterization 2.2 The chirality decomposition of M 2.3 A topological no-go theorem 2.4 The singular distribution D 2.5 Spinor parameterization and G 2 structure on the non-chiral locus 2.6 Spinor parameterization and Spin(7) ± structures on the loci U ± 2.7 Comparing spinors and G structures on the non-chiral locus 2.8 The singular foliation of M defined by D 3 Relating the G 2 and Spin(7) approaches on the non-chiral locus 3.1 The G 2 and Spin(7) ± decompositions of Ω 4 (U) 3.2 The G 2 and Spin(7) ± parameterizations of F 3.3 Relating the G 2 torsion classes to the Lee form and characteristic torsion of the Spin(7) ± structures 3.4 Relation to previous work 4 Description of the singular foliation in the Morse case 4.1 Types of singular points 4.2 The regular and singular foliations defined by a Morse 1-form 4.3 Behavior of the singular leaves near singular points 4.4 Combinatorics of singular leaves 4.5 Homology classes of compact leaves 4.6 The Novikov decomposition of M 4.7 The foliation graph 4.8 The fundamental group of the leaf space 4.9 On the relation to compactifications of M-theory on 7-manifolds 4.10 A non-commutative description of the leaf space ? 5 Conclusions and further directions A Proof of the topological no-go theorem B The case κ = 0 B.1 When M is compact B.2 When M is non-compact-i-C Comparison with the results of [1] D Generalized bundles and generalized distributions E Some topological properties of singular foliations defined by a Morse oneform E.1 Some topological invariants of M E.2 Estimate for the number of splitting saddle points E.3 Estimates for c and N min E.4 Criteria for existence and number of homologically independent compact leaves E.
The real Jacobi group $G^J_1(\mathbb{R})={\rm SL}(2,\mathbb{R})\ltimes {\rm H}_1$, where ${\rm H}... more The real Jacobi group $G^J_1(\mathbb{R})={\rm SL}(2,\mathbb{R})\ltimes {\rm H}_1$, where ${\rm H}_1$ denotes the 3-dimensional Heisenberg group, is parametrized by the $S$-coordinates $(x,y,\theta,p,q,\kappa)$. We show that the parameter $\eta$ that appears passing from Perelomov's un-normalized coherent state vector based on the Siegel--Jacobi disk $\mathcal{D}^J_1$ to the normalized one is $\eta=q+\rm{i} p$. The two-parameter invariant metric on the Siegel--Jacobi upper half-plane $\mathcal{X}^J_1=\frac{G^J_1(\R)}{\rm{SO}(2)\times\mathbb{R}}$ is expressed in the variables $(x,y,\rm{Re}~\eta,\rm{Im}~\eta)$. It is proved that the five dimensional manifold $\tilde{\mathcal{X}}^J_1=\frac{G^J_1(\R)}{\rm{SO}(2)}\approx\mathcal{X}^J_1\times\mathbb{R}$, called extended Siegel--Jacobi upper half-plane, is a reductive, non-symmetric, non-naturally reductive manifold with respect to the three-parameter metric invariant to the action of $G^J_1(\mathbb{R})$, and its geodesic vectors are de...
We describe a mathematically rigorous differential model for B-type open-closed topological Landa... more We describe a mathematically rigorous differential model for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is a non-compact K\"ahlerian manifold with holomorphically trivial canonical line bundle and $W$ is a complex-valued holomorphic function defined on $X$ and whose critical locus is compact but need not consist of isolated points. We also show how this construction specializes to the case when $X$ is Stein and $W$ has finite critical set, in which case one recovers a simpler mathematical model.
Springer Proceedings in Mathematics & Statistics, 2018
We propose a class of two-field cosmological models derived from gravity coupled to non-linear si... more We propose a class of two-field cosmological models derived from gravity coupled to non-linear sigma models whose target space is a noncompact and geometrically-finite hyperbolic surface, which provide a wide generalization of so-called α-attractor models and can be studied using uniformization theory. We illustrate cosmological dynamics in such models for the case of the hyperbolic triply-punctured sphere.
Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011), 2012
We studied a relation between the κ-symmetric and the pure spinor formulations of the supermembra... more We studied a relation between the κ-symmetric and the pure spinor formulations of the supermembrane in eleven dimensions using Berkovits' method for the superstring in D=10. Here we attempt to extend this method to the supermembrane showing that it is possible to reinstate the reparameterisation constraints in the pure-spinor formulation of the supermembrane if we introduce a topological sector and performe a similarity transformation. The resulting BRST charge is then of conventional type and is argued to be (related to) the BRST charge of the κ-symmetric supermembrane in a formulation where all second class constraints are 'gauge unfixed' to first class constraints. In this analysis we also encounter a natural candidate for a (non-covariant) supermembrane analogue of the superstring b ghost.
We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the cl... more We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the classification of those two-field cosmological models which admit such symmetries.
Facta universitatis - series: Physics, Chemistry and Technology, 2019
We outline the geometric formulation of cosmological flows for FLRW models with the scalar matter... more We outline the geometric formulation of cosmological flows for FLRW models with the scalar matter as well as certain aspects which arise in their study with methods originating from the geometric theory of dynamical systems. We briefly summarize certain results of numerical analysis which we carried out when the scalar manifold of the model is a hyperbolic surface of the finite or infinite area.
We determine the most general time-independent Noether symmetries of two-field cosmological model... more We determine the most general time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature −3/8, i.e. when the model is of elementary α-attractor type with a fixed value of the parameter α. In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus classifying all models of this type. We also discuss some implications of the corresponding conserved quantity.
We consider the bulk algebra and topological D-brane category arising from the differential model... more We consider the bulk algebra and topological D-brane category arising from the differential model of the open-closed B-type topological Landau-Ginzburg theory defined by a pair (X, W), where X is a non-compact Calabi-Yau manifold and W is a complex-valued holomorphic function. When X is a Stein manifold (but not restricted to be a domain of holomorphy) we extract equivalent descriptions of the bulk algebra and of the category of topological D-branes which are constructed using only the analytic space associated to X. In particular, we show that the D-brane category is described by projective factorizations defined over the ring of holomorphic functions of X. We also discuss simplifications of the analytic models which arise when X is holomorphically parallelizable and illustrate these in a few classes of examples.
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg the... more We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X, W), where X is any non-compact Calabi-Yau manifold and W is any holomorphic complex-valued function defined on X whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector-valued forms and a twisted Dolbeault category of holomorphic factorizations of W. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed TFT (topological field theory) are satisfied on cohomology and conjecture that the remaining two axioms (namely non-degeneracy of bulk and boundary traces and the topological Cardy constraint) are also satisfied.
We study Noether symmetries in two-field cosmological α-attractors, investigating the case when t... more We study Noether symmetries in two-field cosmological α-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincaré disk. We solve the conditions for the existence of a ‘separated’ Noether symmetry and find the form of the scalar potential compatible with such, for any elementary hyperbolic surface. For this class of symmetries, we find that the α-parameter must have a fixed value. Using those Noether symmetries, we also obtain many exact solutions of the equations of motion of these models, which were studied previously with numerical methods.
We consider generalizedα-attractor models whose scalar potentials are globally well-behaved and w... more We consider generalizedα-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré diskD, such surfaces include the hyperbolic punctured diskD⁎and the hyperbolic annuliA(R)of modulusμ=2logR>0. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all three cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. For certain simple but natural choices of extended potentials, we compute scalar field trajectories by projecting numerical solutions of the lifted equations of motion from the Poincaré half plane through the uniformization map, thus illustrating the rich cosmological dynamics of such models.
Supersymmetry-preserving backgrounds in supergravity and string theory can be studied using a pow... more Supersymmetry-preserving backgrounds in supergravity and string theory can be studied using a powerful framework based on a natural realization of Clifford bundles. We explain the geometric origin of this framework and show how it can be used to formulate a theory of 'constrained generalized Killing forms', which gives a useful geometric translation of supersymmetry conditions in the presence of fluxes. Contents 1 The geometric algebra approach to (s)pinors 1 2 Application to general N = 2 flux compactifications of eleven-dimensional supergravity on eight-manifolds. 6
We study the relation between the kappa-symmetric formulation of the supermembrane in eleven dime... more We study the relation between the kappa-symmetric formulation of the supermembrane in eleven dimensions and the pure-spinor version. Recently, Berkovits related the Green-Schwarz and pure-spinor superstrings. In this paper, we attempt to extend this method to the supermembrane. We show that it is possible to reinstate the reparameterisation constraints in the pure-spinor formulation of the supermembrane by introducing a topological sector and performing a similarity transformation. The resulting BRST charge is then of conventional type and is argued to be (related to) the BRST charge of the kappa-symmetric supermembrane in a formulation where all second class constraints are \u27gauge unfixed\u27 to first class constraints. In our analysis we also encounter a natural candidate for a (non-covariant) supermembrane analogue of the superstring b ghost
Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of... more Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through Kähler-Atiyah bundles, which we developed in previous work. Applying this to the most general N = 2 flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.
We investigate the most general warped compactification of eleven-dimensional supergravity on eig... more We investigate the most general warped compactification of eleven-dimensional supergravity on eight-dimensional manifolds to AdS 3 spaces (in the presence of non-vanishing four-form flux) which preserves N = 2 supersymmetry in three dimensions. Without imposing any restrictions on the chirality of the internal part of the supersymmetry generators, we use geometric algebra techniques to study some implications of the supersymmetry constraints. In particular, we discuss the Lie bracket of certain vector fields constructed as pinor bilinears on the compactification manifold.
Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of... more Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through Kähler-Atiyah bundles, which we developed in previous work. Applying this to the most general N = 2 flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.
We show how supersymmetry conditions for flux compactifications of supergravity and string theory... more We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kähler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory compactifications on eight-manifolds down to AdS 3 spaces which preserve N = 2 supersymmetry in 3 dimensions. We also give a brief sketch of the lift of such equations to the cone over the compactification space and of the geometric algebra approach to 'constrained generalized Killing pinors', which forms the technical and conceptual core of our investigation.
We use the theory of singular foliations to study N = 1 compactifications of elevendimensional su... more We use the theory of singular foliations to study N = 1 compactifications of elevendimensional supergravity on eight-manifolds M down to AdS 3 spaces, allowing for the possibility that the internal part ξ of the supersymmetry generator is chiral on some locus W which does not coincide with M. We show that the complement M \ W must be a dense open subset of M and that M admits a singular foliationF endowed with a longitudinal G 2 structure and defined by a closed one-form ω, whose geometry is determined by the supersymmetry conditions. The singular leaves are those leaves which meet W. When ω is a Morse form, the chiral locus is a finite set of points, consisting of isolated zero-dimensional leaves and of conical singularities of seven-dimensional leaves. In that case, we describe the topology ofF using results from Novikov theory. We also show how this description fits in with previous formulas which were extracted by exploiting the Spin(7) ± structures which exist on the complement of W. Contents 1 Basics 2 Parameterizing a Majorana spinor on M 2.1 Globally valid parameterization 2.2 The chirality decomposition of M 2.3 A topological no-go theorem 2.4 The singular distribution D 2.5 Spinor parameterization and G 2 structure on the non-chiral locus 2.6 Spinor parameterization and Spin(7) ± structures on the loci U ± 2.7 Comparing spinors and G structures on the non-chiral locus 2.8 The singular foliation of M defined by D 3 Relating the G 2 and Spin(7) approaches on the non-chiral locus 3.1 The G 2 and Spin(7) ± decompositions of Ω 4 (U) 3.2 The G 2 and Spin(7) ± parameterizations of F 3.3 Relating the G 2 torsion classes to the Lee form and characteristic torsion of the Spin(7) ± structures 3.4 Relation to previous work 4 Description of the singular foliation in the Morse case 4.1 Types of singular points 4.2 The regular and singular foliations defined by a Morse 1-form 4.3 Behavior of the singular leaves near singular points 4.4 Combinatorics of singular leaves 4.5 Homology classes of compact leaves 4.6 The Novikov decomposition of M 4.7 The foliation graph 4.8 The fundamental group of the leaf space 4.9 On the relation to compactifications of M-theory on 7-manifolds 4.10 A non-commutative description of the leaf space ? 5 Conclusions and further directions A Proof of the topological no-go theorem B The case κ = 0 B.1 When M is compact B.2 When M is non-compact-i-C Comparison with the results of [1] D Generalized bundles and generalized distributions E Some topological properties of singular foliations defined by a Morse oneform E.1 Some topological invariants of M E.2 Estimate for the number of splitting saddle points E.3 Estimates for c and N min E.4 Criteria for existence and number of homologically independent compact leaves E.
The real Jacobi group $G^J_1(\mathbb{R})={\rm SL}(2,\mathbb{R})\ltimes {\rm H}_1$, where ${\rm H}... more The real Jacobi group $G^J_1(\mathbb{R})={\rm SL}(2,\mathbb{R})\ltimes {\rm H}_1$, where ${\rm H}_1$ denotes the 3-dimensional Heisenberg group, is parametrized by the $S$-coordinates $(x,y,\theta,p,q,\kappa)$. We show that the parameter $\eta$ that appears passing from Perelomov's un-normalized coherent state vector based on the Siegel--Jacobi disk $\mathcal{D}^J_1$ to the normalized one is $\eta=q+\rm{i} p$. The two-parameter invariant metric on the Siegel--Jacobi upper half-plane $\mathcal{X}^J_1=\frac{G^J_1(\R)}{\rm{SO}(2)\times\mathbb{R}}$ is expressed in the variables $(x,y,\rm{Re}~\eta,\rm{Im}~\eta)$. It is proved that the five dimensional manifold $\tilde{\mathcal{X}}^J_1=\frac{G^J_1(\R)}{\rm{SO}(2)}\approx\mathcal{X}^J_1\times\mathbb{R}$, called extended Siegel--Jacobi upper half-plane, is a reductive, non-symmetric, non-naturally reductive manifold with respect to the three-parameter metric invariant to the action of $G^J_1(\mathbb{R})$, and its geodesic vectors are de...
We describe a mathematically rigorous differential model for B-type open-closed topological Landa... more We describe a mathematically rigorous differential model for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is a non-compact K\"ahlerian manifold with holomorphically trivial canonical line bundle and $W$ is a complex-valued holomorphic function defined on $X$ and whose critical locus is compact but need not consist of isolated points. We also show how this construction specializes to the case when $X$ is Stein and $W$ has finite critical set, in which case one recovers a simpler mathematical model.
Springer Proceedings in Mathematics & Statistics, 2018
We propose a class of two-field cosmological models derived from gravity coupled to non-linear si... more We propose a class of two-field cosmological models derived from gravity coupled to non-linear sigma models whose target space is a noncompact and geometrically-finite hyperbolic surface, which provide a wide generalization of so-called α-attractor models and can be studied using uniformization theory. We illustrate cosmological dynamics in such models for the case of the hyperbolic triply-punctured sphere.
Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011), 2012
We studied a relation between the κ-symmetric and the pure spinor formulations of the supermembra... more We studied a relation between the κ-symmetric and the pure spinor formulations of the supermembrane in eleven dimensions using Berkovits' method for the superstring in D=10. Here we attempt to extend this method to the supermembrane showing that it is possible to reinstate the reparameterisation constraints in the pure-spinor formulation of the supermembrane if we introduce a topological sector and performe a similarity transformation. The resulting BRST charge is then of conventional type and is argued to be (related to) the BRST charge of the κ-symmetric supermembrane in a formulation where all second class constraints are 'gauge unfixed' to first class constraints. In this analysis we also encounter a natural candidate for a (non-covariant) supermembrane analogue of the superstring b ghost.
We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the cl... more We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the classification of those two-field cosmological models which admit such symmetries.
Facta universitatis - series: Physics, Chemistry and Technology, 2019
We outline the geometric formulation of cosmological flows for FLRW models with the scalar matter... more We outline the geometric formulation of cosmological flows for FLRW models with the scalar matter as well as certain aspects which arise in their study with methods originating from the geometric theory of dynamical systems. We briefly summarize certain results of numerical analysis which we carried out when the scalar manifold of the model is a hyperbolic surface of the finite or infinite area.
We determine the most general time-independent Noether symmetries of two-field cosmological model... more We determine the most general time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature −3/8, i.e. when the model is of elementary α-attractor type with a fixed value of the parameter α. In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus classifying all models of this type. We also discuss some implications of the corresponding conserved quantity.
We consider the bulk algebra and topological D-brane category arising from the differential model... more We consider the bulk algebra and topological D-brane category arising from the differential model of the open-closed B-type topological Landau-Ginzburg theory defined by a pair (X, W), where X is a non-compact Calabi-Yau manifold and W is a complex-valued holomorphic function. When X is a Stein manifold (but not restricted to be a domain of holomorphy) we extract equivalent descriptions of the bulk algebra and of the category of topological D-branes which are constructed using only the analytic space associated to X. In particular, we show that the D-brane category is described by projective factorizations defined over the ring of holomorphic functions of X. We also discuss simplifications of the analytic models which arise when X is holomorphically parallelizable and illustrate these in a few classes of examples.
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg the... more We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X, W), where X is any non-compact Calabi-Yau manifold and W is any holomorphic complex-valued function defined on X whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector-valued forms and a twisted Dolbeault category of holomorphic factorizations of W. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed TFT (topological field theory) are satisfied on cohomology and conjecture that the remaining two axioms (namely non-degeneracy of bulk and boundary traces and the topological Cardy constraint) are also satisfied.
We study Noether symmetries in two-field cosmological α-attractors, investigating the case when t... more We study Noether symmetries in two-field cosmological α-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincaré disk. We solve the conditions for the existence of a ‘separated’ Noether symmetry and find the form of the scalar potential compatible with such, for any elementary hyperbolic surface. For this class of symmetries, we find that the α-parameter must have a fixed value. Using those Noether symmetries, we also obtain many exact solutions of the equations of motion of these models, which were studied previously with numerical methods.
We consider generalizedα-attractor models whose scalar potentials are globally well-behaved and w... more We consider generalizedα-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré diskD, such surfaces include the hyperbolic punctured diskD⁎and the hyperbolic annuliA(R)of modulusμ=2logR>0. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all three cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. For certain simple but natural choices of extended potentials, we compute scalar field trajectories by projecting numerical solutions of the lifted equations of motion from the Poincaré half plane through the uniformization map, thus illustrating the rich cosmological dynamics of such models.
Supersymmetry-preserving backgrounds in supergravity and string theory can be studied using a pow... more Supersymmetry-preserving backgrounds in supergravity and string theory can be studied using a powerful framework based on a natural realization of Clifford bundles. We explain the geometric origin of this framework and show how it can be used to formulate a theory of 'constrained generalized Killing forms', which gives a useful geometric translation of supersymmetry conditions in the presence of fluxes. Contents 1 The geometric algebra approach to (s)pinors 1 2 Application to general N = 2 flux compactifications of eleven-dimensional supergravity on eight-manifolds. 6
We study the relation between the kappa-symmetric formulation of the supermembrane in eleven dime... more We study the relation between the kappa-symmetric formulation of the supermembrane in eleven dimensions and the pure-spinor version. Recently, Berkovits related the Green-Schwarz and pure-spinor superstrings. In this paper, we attempt to extend this method to the supermembrane. We show that it is possible to reinstate the reparameterisation constraints in the pure-spinor formulation of the supermembrane by introducing a topological sector and performing a similarity transformation. The resulting BRST charge is then of conventional type and is argued to be (related to) the BRST charge of the kappa-symmetric supermembrane in a formulation where all second class constraints are \u27gauge unfixed\u27 to first class constraints. In our analysis we also encounter a natural candidate for a (non-covariant) supermembrane analogue of the superstring b ghost
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Papers by Mirela Babalic