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C. S. Shahbazi

Publications and source records attributed to C. S. Shahbazi.

At least 55 records · Page 3Linked to original sources
arXiv2016

The global formulation of generalized Einstein-Scalar-Maxwell theories

We 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.

math.DG↗
arXiv2016

Products of multisymplectic manifolds and homotopy moment maps

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L-infinity-embedding of the L-infinity-algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a by-product, we associate to every multisymplectic form a curved L-infinity-algebra, whose curvature is the multisymplectic form itself.

math.DG↗
arXiv2016

M-theory on non-Kähler manifolds

We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of locally conformally Kähler manifolds which locally carry a preferred Calabi-Yau structure.

hep-th↗
arXiv2016

Five-dimensional null & time-like supersymmetric geometries

We show that there exist supersymmetric solutions of five-dimensional, pure, $\mathcal{N}=1$ Supergravity such that the norm of the supersymmetric Killing vector, built out of the Killing spinor, is a real not-everywhere analytic function such that all its derivatives vanish at a point where the Killing vector field becomes null. The norm of the Killing vector field then is not an analytic function on a neighborhood around this point. We explicitly construct such solutions by using a multi-center Gibbons-Hawking base. Although many of these solutions have infinite charges, we find explicit examples with finite charges that asymptote to $AdS_3\times S_2$ and discuss their physical interpretation.

hep-th↗
arXiv2015

A class of non-geometric M-theory compactification backgrounds

We study a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds to three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is still a differentiable manifold, although with very different geometric and topological properties with respect to the corresponding standard M-theory compactification background: it is a compact complex manifold admitting a Kähler covering with deck transformations acting by holomorphic homotheties with respect to the Kähler metric. We show that this class of non-geometric compactifications evade the Maldacena-Nuñez no-go theorem by means of a mechanism originally developed by Mario García-Fernández and the author for Heterotic Supergravity, and thus do not require $l_{P}$-corrections to allow for a non-trivial warp factor or four-form flux. We obtain an explicit compactification background on a complex Hopf four-fold that solves all the equations of motion of the theory. We also show that this class of non-geometric compactification backgrounds is equipped with a holomorphic principal torus fibration over a projective Kähler base as well as a codimension-one foliation with nearly-parallel $G_{2}$-leaves, making thus contact with the work of M. Babalic and C. Lazaroiu on the foliation structure of the most general M-theory supersymmetric compactifications.

hep-th↗
arXiv2015

Self-dual generalized metrics for pure $\mathcal{N}=1$ six-dimensional Supergravity

We geometrize six-dimensional pure $\mathcal{N}=1$ Supergravity by means of an exact Courant algebroid, whose Severa class is defined through the Supergravity three-form $H$, equipped with a generalized metric and a compatible, torsion-free, generalized connection. The Supergravity equations of motion follow from the vanishing of the Ricci curvature of the generalized metric, satisfying a natural notion of self-duality. This way, we interpret the solutions of six-dimensional pure, $\mathcal{N}=1$, Supergravity as generalized self-dual gravitational monopoles. For the D1-D5 black string solution, we explore the possibility of controlling space-time singularities by using $B$-field transformations.

hep-th↗
arXiv2015

M-theory moduli spaces and torsion-free structures

Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of $Spin(7)$-structures on an eight-dimensional $S^{1}$-bundle to the set of $G_{2}$-structures on the base space, fully characterizing the $G_{2}$-torsion clases when the total space is equipped with a torsion-free $Spin(7)$-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of M-theory compactifications.

hep-th↗
arXiv2015

Non-extremal branes

We prove that for arbitrary black brane solutions of generic Supergravities there is an adapted system of variables in which the equations of motion are exactly invariant under electric-magnetic duality, i.e. the interchange of a given extended object by its electromagnetic dual. We obtain thus a procedure to automatically construct the electromagnetic dual of a given brane without needing to solve any further equation. We apply this procedure to construct the non-extremal (p, q)-string of Type-IIB String Theory (new in the literature), explicitly showing how the dual (p, q)-five-brane automatically arises in this construction. In addition, we prove that the system of variables used is suitable for a generic characterization of every double-extremal Supergravity brane solution, which we perform in full generality.

hep-th↗
arXiv2014

Spin(7)-manifolds in compactifications to four dimensions

We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold $\mathcal{M}_{8}$ equipped with a particular set of tensors $\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ a family of $G_{2}$-structure seven-dimensional manifolds as the leaves of a codimension-one foliation. Under a different set of assumptions, $\mathfrak{S}$ allows to make $\mathcal{M}_{8}$ into a principal $S^{1}$ bundle, which is equipped with a topological $Spin(7)$-structure if the base is equipped with a topological $G_{2}$-structure. We also show that $\mathfrak{S}$ can be naturally used to describe regular as well as a singular elliptic fibrations on $\mathcal{M}_{8}$, which may be relevant for F-theory applications, and prove several mathematical results concerning the relation between topological $G_{2}$-structures in seven dimensions and topological $Spin(7)$-structures in eight dimensions.

hep-th↗
arXiv2014

Regular 3-charge 4D black holes and their microscopic description

The perturbative $α^{\prime}$ corrections to Type-IIA String Theory compactified on a Calabi-Yau three-fold allow the construction of regular three-charge supersymmetric black holes in four dimensions, whose entropy scales with the charges as $S \sim \left( p^1 p^2 p^3\right)^{\frac{2}{3}} $. We construct an M-theory uplift of these quantum black holes and show that they can be interpreted as arising from three stacks of M2 branes on a conical singularity. This in turns allow us relate them via a series of dualities to a system of D3 branes carrying momentum and thus to give a microscopic interpretation of their entropy.

hep-th↗
arXiv2014

Strongly Homotopy Lie Algebras from Multisymplectic Geometry

This Master Thesis is devoted to the study of $n$-plectic manifolds and the Strongly Homotopy Lie algebras, also called $L_{\infty}$-algebras, that can be associated to them. Since multisymplectic geometry and $L_{\infty}$-algebras are relevant in Theoretical Physics, and in particular in String Theory, we introduce the relevant background material in order to make the exposition accessible to non-experts, perhaps interested physicists. The background material includes graded and homological algebra theory, fibre bundles, basics of group actions on manifolds and symplectic geometry. We give an introduction to $L_{\infty}$-algebras and define $L_{\infty}$-morphisms in an independent way, not yet related to multisymplectic geometry, giving explicit formulae relating $L_{\infty}[1]$-algebras and $L_{\infty}$-algebras. We give also an account of multisymplectic geometry and $n$-plectic manifolds, connecting them to $L_{\infty}$-algebras. We then introduce, closely following the work {1304.2051} of Yael Fregier, Christopher L. Rogers and Marco Zambon, the concept of homotopy moment map. The new results presented here are the following: we obtain specific conditions under which two $n$-plectic manifolds with strictly isomorphic Lie-$n$ algebras are symplectomorphic, and we study the construction of an homotopy moment map for a product manifold, assuming that the factors are $n$-plectic manifolds equipped with the corresponding homotopy moment maps.

math.DG↗
arXiv2014

Topological solutions in ungauged Supergravity

A new general class of solutions of ungauged four-dimensional Supegravity, in one-to-one correspondence with spherically symmetric, static black-hole solutions and Lifshitz solutions with Hyperscaling violation (\emph{hvLif}) is studied. The causal structure of the space-time is then elucidated.

hep-th↗
arXiv2013

The violation of the No-Hair Conjecture in four-dimensional ungauged Supergravity

By choosing a particular, String Theory inspired, Special Kähler manifold, we are able to find a N=2 four-dimensional ungauged Supergravity model that contains supersymmetric black hole solutions that violate the folk uniqueness theorems that are expected to hold in ungauged Supergravity. The black hole solutions are regular in the sense that they have a positive mass and a unique physical singularity hidden by an event horizon. In contradistinction to most examples already known in the literature, we find our solutions in a theory without scalar potential, gaugings or higher order curvature terms.

hep-th↗
arXiv2013

Non-perturbative black holes in Type-IIA String Theory vs. the No-Hair conjecture

We obtain the first black hole solution to Type-IIA String Theory compactified on an arbitrary self-mirror Calabi Yau manifold in the presence of non-perturbative quantum corrections. Remarkably enough, the solution involves multivalued functions, which could lead to a violation of the No-Hair conjecture. We discuss how String Theory forbids such secenario. However the possibility still remains open in the context of four-dimensional ungauged Supergravity.

hep-th↗
arXiv2013

On hvLif-like solutions in gauged Supergravity

We perform a thorough investigation of Lifshitz-like metrics with hyperscaling violation (hvLif) in four-dimensional theories of gravity coupled to an arbitrary number of scalars and vector fields, obtaining new solutions, electric, magnetic and dyonic, that include the known ones as particular cases. After establishing some general results on the properties of purely hvLif solutions, we apply the previous formalism to the case of \mathcal{N}=2, d=4 Supergravity in the presence of Fayet-Iliopoulos terms, obtaining particular solutions to the t^3-model, and explicitly embedding some of them in Type-IIB String Theory.

hep-th↗
arXiv2013

Black Holes in Supergravity with Applications to String Theory

This thesis is devoted to the study of black hole solutions in ungauged four-dimensional extended Supergravity. We characterize the most general spherically symmetric and static black-hole solution of ungauged Supergravity, and use the result to study the hidden conformal symmetries of Supergravity black holes, obtaining the full Virasoro algebra of the dual conformal field theory. We obtain also all the supersymmetric black-hole metrics of all extended Supergravities using the properties of the groups of Type E7. We introduce the H-F.G.K. formalism, which simplifies the construction of non-supersymmetric black-hole solutions in N=2 Supergravity, and apply it to a class of theories corresponding to Type-IIA String Theory compactified on a Calabi-Yau threefold. As a result we obtain the so-called "quantum" black holes, which only exist when certain quantum corrections (perturbative or non-perturbative, depending on the solution) are included in the prepotential. For the case of non-perturbative black holes, we elaborate on the potential consequences of the appearance on the solution of multi-valued functions in relation to the no-hair theorem for four-dimensional black holes. This thesis also contains the relevant mathematical background to formulate extended ungauged Supergravity in four-dimensions, that is, Special Kähler Geometry and homogeneous spaces, as well as a brief introduction to the mathematical structure of four-dimensional extended ungauged Supergravity.

hep-th↗
arXiv2013

Dirac-Born-Infeld-Volkov-Akulov and Deformation of Supersymmetry

We deform the action and the supersymmetry transformations of the d=10 and d=4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d=6 vector branes related to chiral (2,0) supergravity, which we denote as `Vp-branes'. We use a space-filling V5 superbrane for the d=6 model and a V3 superbrane for the d=4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d=10 and 4, and half-maximal 8+8 supersymmetries in d=6 and 4.

hep-th↗