27 research outputs found
Generalized two-field α-attractor models from geometrically finite hyperbolic surfaces
We consider four-dimensional gravity coupled to a non-linear sigma model whose scalar manifold is a non-compact geometrically finite surface Σ endowed with a Riemannian metric of constant negative curvature. When the space-time is an FLRW universe, such theories produce a very wide generalization of two-field α-attractor models, being parameterized by a positive constant α, by the choice of a finitely-generated surface group Γ⊂PSL(2,R) (which is isomorphic with the fundamental group of Σ) and by the choice of a scalar potential defined on Σ. The traditional two-field α-attractor models arise when Γ is the trivial group, in which case Σ is the Poincaré disk. We give a general prescription for the study of such models through uniformization in the so-called “non-elementary” case and discuss some of their qualitative features in the gradient flow approximation, which we relate to Morse theory. We also discuss some aspects of the SRST approximation in these models, showing that it is generally not well-suited for studying dynamics near cusp ends. When Σ is non-compact and the scalar potential is “well-behaved” at the ends, we show that, in the naive local one-field truncation, our generalized models have the same universal behavior as ordinary one-field α-attractors if inflation happens near any of the ends of Σ where the extended potential has a local maximum, for trajectories which are well approximated by non-canonically parameterized geodesics near the ends; we also discuss spiral trajectories near the ends. Generalized two field α-attractors illustrate interesting consequences of nonlinear sigma models whose scalar manifold is not simply connected. They provide a large class of tractable cosmological models with non-trivial topology of the scalar field space. © 2018 The Author(s
H-FGK formalism for black-hole solutions of N=2, d=4 and d=5 supergravity
We rewrite the Ferrara-Gibbons-Kallosh (FGK) black-hole effective action of
N=2, d=4,5 supergravities coupled to vector multiplets, replacing the metric
warp factor and the physical scalars with real variables that transform in the
same way as the charges under duality transformations, which simplifies the
equations of motion. For a given model, the form of the solution in these
variables is the same for all spherically symmetric black holes, regardless of
supersymmetry or extremality.Comment: 10 pages; v2: references added, some editing of the text, results
unchanged; v3: references added as in the published versio
Generalized two-field α-attractor models from geometrically finite hyperbolic surfaces
We consider four-dimensional gravity coupled to a non-linear sigma model whose scalar manifold is a non-compact geometrically finite surface Σ endowed with a Riemannian metric of constant negative curvature. When the space-time is an FLRW universe, such theories produce a very wide generalization of two-field α-attractor models, being parameterized by a positive constant α, by the choice of a finitely-generated surface group Γ⊂PSL(2,R) (which is isomorphic with the fundamental group of Σ) and by the choice of a scalar potential defined on Σ. The traditional two-field α-attractor models arise when Γ is the trivial group, in which case Σ is the Poincaré disk. We give a general prescription for the study of such models through uniformization in the so-called “non-elementary” case and discuss some of their qualitative features in the gradient flow approximation, which we relate to Morse theory. We also discuss some aspects of the SRST approximation in these models, showing that it is generally not well-suited for studying dynamics near cusp ends. When Σ is non-compact and the scalar potential is “well-behaved” at the ends, we show that, in the naive local one-field truncation, our generalized models have the same universal behavior as ordinary one-field α-attractors if inflation happens near any of the ends of Σ where the extended potential has a local maximum, for trajectories which are well approximated by non-canonically parameterized geodesics near the ends; we also discuss spiral trajectories near the ends. Generalized two field α-attractors illustrate interesting consequences of nonlinear sigma models whose scalar manifold is not simply connected. They provide a large class of tractable cosmological models with non-trivial topology of the scalar field space
The global formulation of generalized Einstein-Scalar-Maxwell theories
International audienceWe summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such models, which consists of flat unbased symplectic automorphisms of the flat symplectic vector bundle lifting those isometries of the scalar manifold which preserve the scalar potential. The Dirac quantization condition for such models involves a local system of integral symplectic spaces, giving rise to a bundle of polarized Abelian varieties equipped with a symplectic flat connection, which is defined over the scalar manifold of the theory. Generalized Einstein-Scalar-Maxwell models arise as the bosonic sector of the effective theory of string/M-theory compactifications to four-dimensions, and they are characterized by having non-trivial solutions of “U-fold” type
Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds
International audienc
Complex Lipschitz structures and bundles of complex Clifford modules
Let (M,g) be a pseudo-Riemannian manifold of signature (p,q). We construct mutually quasi-inverse equivalences between the groupoid of bundles of weakly-faithful complex Clifford modules on (M,g) and the groupoid of reduced complex Lipschitz structures on (M,g). As an application, we show that (M,g) admits a bundle of irreducible complex Clifford modules if and only if it admits either a Spinc(p,q) structure (when p+q is odd) or a Pinc(p,q) structure (when p+q is even). When p−q≡83,4,6,7, we compare with the classification of bundles of irreducible real Clifford modules which we obtained in previous work. The results obtained in this note form a counterpart of the classification of bundles of faithful complex Clifford modules which was previously given by T. Friedrich and A. Trautman. © 2018 Elsevier B.
Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds
We give the global mathematical formulation of the coupling of four-dimensional scalar
sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation
when the duality structure of the Abelian gauge theory is described by a flat symplectic vector
bundle (S, D, ω) defined over the scalar manifold M. The construction uses a taming of (S, ω), which
we find to be the correct mathematical object globally encoding the inverse gauge couplings and
theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames.
We show that global solutions of the equations of motion of such models give classical locally
geometric U-folds. We also describe the groups of duality transformations and
scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of M to
the bundle S and hence differ from expectations based on local analysis. The appropriate version of
the Dirac quantization condition involves a discrete local system defined over M and gives rise to a
smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows,
in particular, that a generalization of part of the mathematical structure familiar from N = 2 supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetr
Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds
We give the global mathematical formulation of a class of generalized four-dimensional
theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories,
the scalar fields are described by a section of a surjective pseudo-Riemannian submersion
π over space–time, whose total space carries a Lorentzian metric making the fibers into
totally-geodesic connected Riemannian submanifolds. In particular, π is a fiber bundle
endowed with a complete Ehresmann connection whose transport acts through isometries
between the fibers. In turn, the Abelian gauge fields are ‘‘twisted’’ by a flat symplectic vector
bundle defined over the total space of π. This vector bundle is endowed with a vertical
taming which locally encodes the gauge couplings and theta angles of the theory and gives
rise to the notion of twisted self-duality, of crucial importance to construct the theory.
When the Ehresmann connection of π is integrable, we show that our theories are locally
equivalent to ordinary Einstein-Scalar-Maxwell theories and hence provide a global nontrivial
extension of the universal bosonic sector of four-dimensional supergravity. In this
case, we show using a special trivializing atlas of π that global solutions of such models
can be interpreted as classical ‘‘locally-geometric’’ U-folds. In the non-integrable case, our
theories differ locally from ordinary Einstein-Scalar-Maxwell theories and may provide a
geometric description of classical U-folds which are ‘‘locally non-geometric’’.© 2018 Elsevier B.V. All rights reserved.11sci
N=2 Supergravity Counterterms, Off and On Shell
We study N=2 supergravity deformed by a genuine supersymmetric completion of the term, using the underlying off shell N=2 superconformal framework. The gauge-fixed superconformal model has unbroken local supersymmetry of N=2 supergravity with higher derivative deformation. Elimination of auxiliary fields leads to the deformation of the supersymmetry rules as well as to the deformation of the action, which becomes a Born-Infeld with higher derivative type action. We find that the gravitino supersymmetry deformation starts from \lambda \, \pa^4 {\cal F}^3 and has higher graviphoton couplings. In the action there are terms \lambda^2 \pa^8 {\cal F}^{6} and higher, in addition to original on shell counterterm deformation. These deformations are absent in the on shell superspace and in the candidate on shell counterterms of N=4,~8 supergravities, truncated down to N=2. We conclude therefore that the undeformed on shell superspace candidate counterterms break the N=2 part of local supersymmetry.We study N=2 supergravity deformed by a genuine supersymmetric completion of the term, using the underlying off shell N=2 superconformal framework. The gauge-fixed superconformal model has unbroken local supersymmetry of N=2 supergravity with higher derivative deformation. Elimination of auxiliary fields leads to the deformation of the supersymmetry rules as well as to the deformation of the action, which becomes a Born-Infeld with higher derivative type action. We find that the gravitino supersymmetry deformation starts from \lambda \, \pa^4 {\cal F}^3 and has higher graviphoton couplings. In the action there are terms \lambda^2 \pa^8 {\cal F}^{6} and higher, in addition to original on shell counterterm deformation. These deformations are absent in the on shell superspace and in the candidate on shell counterterms of N=4,~8 supergravities, truncated down to N=2. We conclude therefore that the undeformed on shell superspace candidate counterterms break the N=2 part of local supersymmetry