arXiv subjects

Mario Trigiante

Publications and source records attributed to Mario Trigiante.

At least 37 records · Page 2Linked to original sources

arXiv2023

New Torsional Deformations of Locally AdS$_3$ Space

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations for the Riemann curvature and torsion. These geometries involve a peculiar interplay between the vector $(β_i)$ and the singlet $(τ)$ irreducible components of the torsion which, under general conditions, feature a formal analogy with the equation for a Beltrami fluid. Interestingly, we find that the local AdS$_3$ geometry is now deformed by effect of the "Beltrami-torsion" $β_i$. Some of these new solutions describe deformations of the BTZ black hole due to the presence of torsion. The latter acts as a geometric flux which, in some cases, removes the causal singularity.

hep-th↗

arXiv2023

D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler-Einstein surfaces

D3-brane solutions of type IIB supergravity can be obtained by means a classical ansatz involving a harmonic warp factor and two summands, the first being the flat Minkowskian metric of the D3 brane world-sheet and the second a Ricci flat metric on a suitable 6-dimensional transverse space, both twisted by the warp factor. Of particular interest is the case of the total space of thecanonical bundle over a complex Kähler 2-fold. This situation emerges in many cases while considering the resolution of finite quotient singulaties. When the group is $\mathbb{Z}_4$, the complex 2-fold is the second Hirzebruch surface endowed with a Kähler metric having SU(2)xU(1) isometry. There is actually an entire class of such metrics parameterized by a single function, and best described in the AMSY symplectic formalism. We recover the existence of a two parameter subclass of Kähler-Einstein metrics on manifolds that are homeorphic to $S^2\times S^2$, and study in detail this class. The K"ahler-Einstein nature of these manifolds allows the construction of the Ricci flat metric on their canonical bundle via the Calabi Ansatz, which we recast in the AMSY formalism deriving some new elegant formulae. Furthermore we show the full integrability of the differential system of geodesics equations thanks to an additional conserved quantity that we unveil and which is similar to the Carter constant in the case of the Kerr metric.

math-ph↗

arXiv2023

Gauged D=4 N=4 Supergravity

We present the full Lagrangian and supersymmetry transformation rules for the gauged D=4, N=4 (half-maximal) supergravity coupled to an arbitrary number of vector multiplets. Using the embedding tensor formulation, the final results are universal and valid in arbitrary symplectic frames. We also analyze the conditions for the critical points of the scalar potential and specify the full spectrum of the quadratic fluctuations about Minkowski vacua. This allows us also to exclude the appearance of quadratic divergences in the 1-loop corrections to the scalar potential for any Minkowski vacuum fully breaking supersymmetry. We also provide some interesting byproducts of our analysis, like the field equations and the quadratic constraints for the fermion shifts characterizing the gauging (also known as T-tensor identities).

hep-th↗

arXiv2023

Chaos from Symmetry: Navier Stokes equations, Beltrami fields and the Universal Classifying Crystallographic Group

The core of this paper is a novel group-theoretical approach, initiated in 2015 by one of the present authors in collaboration with Alexander Sorin, which allows for a more systematic classification and algorithmic construction of Beltrami flows on torii $\mathbb{R}^3/Λ$ where $Λ$ is a crystallographic lattice. The new hydro-theory, based on the idea of a Universal Classifying Group $\mathfrak{UG}_Λ$, is here revised. We construct the so far missing $\mathfrak{UG}_{Λ_{Hex}}$ for the hexagonal lattice. Mastering the cubic and hexagonal instances, we can cover all cases. The classification relation between Beltrami Flows and contact structures is enlightened. The most promising research direction opened by the present work streams from the fact that the Fourier series expansion of a generic Navier-Stokes solution can be regrouped into an infinite sum of contributions $\mathbf{W}_r$, each associated with a spherical layer of quantized radius $r$ in the momentum lattice and consisting of a superposition of a Beltrami and an anti-Beltrami field, with an analogous decomposition into irreps of the group $\mathfrak{UG}_Λ$ that are variously repeated on higher layers. This crucial property enables the construction of generic Fourier series with prescribed hidden symmetries as candidate solutions of the NS equations. As a further result of this research programme a complete and versatile system of MATHEMATICA Codes named \textbf{AlmafluidaNSPsystem} has been constructed and is now available through the site of the Wolfram Community. The main message streaming from our constructions is that the more symmetric the Beltrami Flow the highest is the probability of the onset of chaotic trajectories.

nlin.CD↗

arXiv2023

Holographic Evidence for Non-Supersymmetric Conformal Manifolds

We provide the first holographic evidence for the existence of a non-supersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter non-supersymmetric deformation of a supersymmetric AdS non-geometric background in Type IIB string theory. We prove that the non-supersymmetric backgrounds are perturbatively stable and also do not suffer from various non-perturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

hep-th↗

arXiv2023

Supersymmetric solitons in gauged $\mathcal{N}=8$ supergravity

We consider soliton solutions in AdS$_{4}$ with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged $\mathcal{N}=8$ supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, there exists a non-supersymmetric soliton solution with energy lower than the supersymmetric one.

hep-th↗

arXiv2022

Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua

We analyze the vacuum structure of $\mathcal{N}=3,D=4$ supergravity coupled to 9 vector multiplets with gauge group ${\rm SO}(3)\times {\rm SU}(3)$. Aside from the central $\mathcal{N}=3$ AdS$_4$ vacuum at the origin, on which the supermultiplet structure reproduces the massless sector of M-theory compactified on $\mathrm{N^{0,1,0}}$, we find a rich structure of AdS$_4$ vacua preserving $\mathcal{N}=0,1,2,3$ supersymmetry. These new vacua are arranged in a manifold spanned by scalar fields corresponding to exactly marginal deformations of the dual CFT. This manifold has the form $T^3/K$, where $K$ is a discrete subgroup of the gauge group: $\mathcal{N}=3,2$ and $1$ vacua correspond, respectively, to a point, a line and a surface in the three-dimensional vacuum manifold. We study RG flows from the central $\mathcal{N}=3$ vacuum and elaborate on the possible higher dimensional origin of the new vacua. For the reader's convenience we also provide a review of the embedding tensor formulation of $D=4$, $\mathcal{N}=3$ gauged supergravities. In particular we provide formulas involving the fermion shift tensors and mass matrices in $\mathcal{N}=3$ theories, which can be applied to a generic gauging.

hep-th↗

arXiv2022

Gauged Supergravities

We give a general review of extended supergravities and their gauging using the duality-covariant embedding tensor formalism. Although the focus is on four-dimensional theories, an overview of the gauging procedure and the related tensor hierarchy in the higher-dimensional models is given. The relation of gauged supergravities to flux compactifications is discussed and examples are worked out in detail.

hep-th↗

arXiv2021

Instability of supersymmetric black holes via quantum phase transitions

In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\,\mathcal{N}=2$ supergravity theories interpolating between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\,\mathcal{N}=8$ supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable choices of the parameters defining the $\,\mathcal{N}=2$ model, the supersymmetric solution features a higher free energy than the non-supersymmetric one. In the absence of additional selection rules, this would imply an instability of the supersymmetric configuration, hinting towards a possible supersymmetry breaking mechanism.

hep-th↗

arXiv2021

Global Properties of the Conformal Manifold for S-Fold Backgrounds

We study a one-parameter family of $\mathcal{N}=2$ anti-de Sitter vacua with ${\rm U}(1)^2$ symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group $[{\rm SO}(6)\times {\rm SO}(1,1)]\ltimes \mathbb{R}^{12}$. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology $S^1\times S^5$. The family of AdS$_4$ vacua is parametrized by a modulus $χ$. Although $χ$ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $\frac{2π}{T}$, which is the inverse radius of $S^1$. We deduce this by providing the explicit $D=10$ uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of $χ$. At the special values $χ=0$ and $χ=\fracπ{T}$, the symmetry enhances according to ${\rm U}(1)^2\rightarrow{\rm U}(2)$, giving rise however to inequivalent Kaluza-Klein spectra. At $χ=\fracπ{T}$, this realizes a bosonic version of the "space invaders" scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

hep-th↗

arXiv2021

$\mathcal{N}=2$ supersymmetric S-folds

Multi-parametric families of AdS$_{4}$ vacua with various amounts of supersymmetry and residual gauge symmetry are found in the $\,[\textrm{SO}(1,1) \times \textrm{SO}(6)] \ltimes \mathbb{R}^{12}\,$ maximal supergravity that arises from the reduction of type IIB supergravity on $\,\mathbb{R} \times \textrm{S}^5\,$. These provide natural candidates to holographically describe new strongly coupled three-dimensional CFT's which are localised on interfaces of $\,\mathcal{N}=4\,$ super-Yang--Mills theory. One such AdS$_{4}$ vacua features a symmetry enhancement to $\,\textrm{SU}(2) \times \textrm{U}(1)\,$ while preserving $\,\mathcal{N}=2\,$ supersymmetry. Fetching techniques from the $\,\textrm{E}_{7(7)}\,$ exceptional field theory, its uplift to a class of $\,\mathcal{N}=2\,$ S-folds of type IIB supergravity of the form $\,\textrm{AdS}_{4} \times \textrm{S}^{1} \times \textrm{S}^5\,$ involving S-duality twists of hyperbolic type along $\,\textrm{S}^{1}\,$ is presented.

hep-th↗

arXiv2021

New non-extremal and BPS hairy black holes in gauged $\,\mathcal{N}=2\,$ and $\,\mathcal{N}=8\,$ supergravity

In this article we study a family of four-dimensional, $\mathcal{N}=2$ supergravity theories that interpolates between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\mathcal{N}=8$ supergravity. In this infinitely many theories characterized by two real numbers -- the interpolation parameter and the dyonic "angle" of the gauging -- we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the $\mathcal{N}=8$ theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

hep-th↗

arXiv2021

Exact holographic RG flows in extended SUGRA

We present a family of exact planar hairy neutral black hole solutions in extended supergravity with Fayet-Iliopoulos (FI) terms. We consider a model where the magnetic part of FI sector vanishes and obtain the superpotential at finite temperature in analytic form. Then, we discuss the thermodynamics and some holographic properties of these solutions. We regularize the action by two different methods, one with gravitational and scalar counterterms and the other using the thermal superpotential as a counterterm, and compute the holographic stress tensor. We also construct the $c$-function of the corresponding RG flow and obtain an exact holographic $β$-function for this model.

hep-th↗

arXiv2019

The role of PSL(2,7) in M-theory: M2-branes, Englert equation and the septuples

Reconsidering the M2-brane solutions of d=11 supergravity with a transverse Englert flux introduced by one of us in 2016, we present a new purely group theoretical algorithm to solve Englert equation based on a specific embedding of the PSL(2,7) group into $\mathrm{Weyl[\mathfrak{e}_7]}$. The aforementioned embedding is singled out by the identification of $\mathrm{PSL(2,7)}$ with the automorphism group of the Fano plane. Relying on the revealed intrinsic PSL(2,7) symmetry of Englert equation and on the new algorithm we present an exhaustive classification of Englert fluxes. The residual supersymmetries of the corresponding M2-brane solutions associated with the first of the 8 classes into which we have partitioned Englert fluxes are exhaustively analyzed and we show that all residual d=3 supersymmetries with $\mathcal{N} \in \left\{1,2,3,4,5,6\right\}$ are available. Our constructions correspond to a particular case in the category of M2-brane solutions with transverse self-dual fluxes.

hep-th↗

arXiv2018

Introductory Lectures on Extended Supergravities and Gaugings

In an ungauged supergravity theory, the presence of a \emph{scalar potential} is allowed only for the minimal $\N=1$ case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking supersymmetry only through the so-called \emph{gauging procedure}. The latter consists in promoting a suitable global symmetry group to local symmetry to be gauged by the vector fields of the theory. Gauged supergravities provide a valuable approach to the study of superstring flux-compactifications and the construction of phenomenologically viable, string-inspired models. The aim of these lectures is to give a pedagogical introduction to the subject of gauged supergravities, covering just selected issues and discussing some of their applications.

hep-th↗

arXiv2018

Instantons from geodesics in AdS moduli spaces

We investigate supergravity instantons in Euclidean $\rm AdS_5\times S^5/\mathbb{Z}_k$. These solutions are expected to be dual to instantons of $\mathcal{N}=2$ quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: For degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.

hep-th↗

arXiv2018

Hairy Black Holes and Duality in an Extended Supergravity Model

We consider a $D=4$, $\mathcal{N}=2$ gauged supergravity with an electromagentic Fayet-Iliopoulos term. We restrict to the uncharged, single dilaton consistent truncation and point out that the bulk Lagrangian is self-dual under electromagnetic duality. Within this truncation, we construct two families of exact hairy black hole solutions, which are asymptotically $AdS_4$. When a duality transformation is applied on these solutions, they are mapped to two other inequivalent families of hairy black hole solutions. The mixed boundary conditions of the scalar field correspond to adding a triple-trace operator to the dual field theory action. We also show that the this truncation contains all the consistent single dilaton truncations of gauged $\mathcal{N}=8$ supergravity with a possible $ω$-deformation.

hep-th↗

arXiv2017

Type II origin of dyonic gaugings

Dyonic gaugings of four-dimensional supergravity typically exhibit a richer vacuum structure compared to their purely electric counterparts, but their higher-dimensional origin often remains more mysterious. We consider a class of dyonic gaugings with gauge groups of the type (SO(p,q)xSO(p',q'))$\ltimes N$ with $N$ nilpotent. Using generalized Scherk-Schwarz reductions of exceptional field theory, we show how these four-dimensional gaugings may be consistently embedded in Type II supergravity upon compactification around products of spheres and hyperboloids. As an application, we give the explicit uplift of the N=4 AdS$_4$ vacuum of the theory with gauge group (SO(6)xSO(1,1))$\ltimes T^{12}$ into a supersymmetric AdS$_4$x$M_5$x$S^1$ S-fold solution of IIB supergravity. The internal space $M_5$ is a squashed $S^5$ preserving an SO(4)$ \subset $ SO(6) subset of its isometries.

hep-th↗