arXiv subjects

M. Trigiante

Publications and source records attributed to M. Trigiante.

At least 37 records · Page 2Linked to original sources

arXiv2013

Entropy Current Formalism for Supersymmetric Theories

The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to supersymmetric theories and supergravities. We formulate a new entropy current in superspace with the properties: 1) it is conserved off-shell for non dissipative fluids, 2) it is invariant under rigid supersymmetry transformations 3) it is covariantly closed in local supersymmetric theories 4) it reduces to its bosonic expression on space-time.

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arXiv2013

A Note on the Field-Theoretical Description of Superfluids

Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has several interesting aspects. On another side, we have provided in arXiv:1304.2206 a supersymmetric extension of the original works. In the analysis of the Lagrangian structures a new invariant appeared which, although related to known invariants, provides, in our opinion, a better parametrisation of the fluid dynamics in order to describe the fluid/superfluid phases.

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arXiv2012

Evidence for a family of SO(8) gauged supergravity theories

In this note we discuss the classification of duality orbits of N = 8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings and the scalar potential are parameter dependent. We also comment on the possible M-theory uplift and on the meaning of the parameter for the dual gauge theories.

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arXiv2011

Two-Centered Magical Charge Orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product (Q1,Q2), known to control the mutual non-locality of the two centers.

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arXiv2011

Brane solutions and integrability: a status report

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.

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arXiv2010

Black holes in supergravity and integrability

Stationary black holes of massless supergravity theories are described by certain geodesic curves on the target space that is obtained after dimensional reduction over time. When the target space is a symmetric coset space we make use of the group-theoretical structure to prove that the second order geodesic equations are integrable in the sense of Liouville, by explicitly constructing the correct amount of Hamiltonians in involution. This implies that the Hamilton-Jacobi formalism can be applied, which proves that all such black hole solutions, including non-extremal solutions, possess a description in terms of a (fake) superpotential. Furthermore, we improve the existing integration method by the construction of a Lax integration algorithm that integrates the second order equations in one step instead of the usual two step procedure. We illustrate this technology with a specific example.

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arXiv2010

Fake Superpotential for Large and Small Extremal Black Holes

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities. Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov). Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point. This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space. In particular the W function for small non-BPS black holes can always be computed analytically, unlike for the large black-hole case.

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arXiv2009

The full integration of black hole solutions to symmetric supergravity theories

We prove that all stationary and spherical symmetric black hole solutions to theories with symmetric target spaces are integrable and we provide an explicit integration method. This exact integration is based on the description of black hole solutions as geodesic curves on the moduli space of the theory when reduced over the time-like direction. These geodesic equations of motion can be rewritten as a specific Lax pair equation for which mathematicians have provided the integration algorithms when the initial conditions are described by a diagonalizable Lax matrix. On the other hand, solutions described by nilpotent Lax matrices, which originate from extremal regular (small) D = 4 black holes can be obtained as suitable limits of solutions obtained in the diagonalizable case, as we show on the generating geodesic (i.e. most general geodesic modulo global symmetries of the D = 3 model) corresponding to regular (and small) D = 4 black holes. As a byproduct of our analysis we give the explicit form of the Wick rotation connecting the orbits of BPS and non-BPS solutions in maximally supersymmetric supergravity and its STU truncation.

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arXiv2009

First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation

In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides with the Hamilton principal function associated with the one-dimensional effective Lagrangian. This implies that the prepotential can always be defined, at least locally in the radial variable and in the moduli space, both in the extremal and non-extremal case and allows us to conclude that it is duality invariant. We also give, in this framework, a general definition of the ``Weinhold metric'' in terms of which a necessary condition for the existence of multiple attractors is given. The Hamilton-Jacobi formalism can be applied both to the restricted phase space where the electromagnetic potentials have been integrated out as well as in the case where the electromagnetic potentials are dualized to scalar fields using the so-called three-dimensional Euclidean approach. We give some examples of application of the formalism, both for the BPS and the non-BPS black holes.

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arXiv2008

Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds

We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.

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arXiv2008

Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules

We study the gauging of the orthosymplectic algebras OSp(6|4)xSO(2) and its "dual" OSp(2|4)x SO(6), both based on supergravities with the same exceptional coset SO*(12)/U(6), and gauge group SO(6)xSO(2). The two dual theories are obtained by two different truncations of gauged N=8 AdS_4 supergravity. We explicitly study the gauge sector of the two dual theories with the most general group allowed by supersymmetry. In the ungauged (super-Poincaré) case they exhibit the same (large) black-hole attractor solutions with dual relations between the 1/N-BPS and non-BPS configurations. The N=6 gravity multiplet has also the exceptional property to be a {\em zero-center module} of OSp(6|4), as it is the case for superconformal Yang--Mills theory in four dimensions based on SU(2,2|n) (PSU(2,2|4) for n=4) or OSp(n|4).

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arXiv2007

Non-BPS Attractors in 5d and 6d Extended Supergravity

We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.

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arXiv2007

On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds

We derive the complete supergravity description of the N=2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)}$, obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric superpotential $W$ proposed, some time ago, by Berglund and Mayr.

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arXiv2007

Critical points of the Black-Hole potential for homogeneous special geometries

We extend the analysis of N=2 extremal Black-Hole attractor equations to the case of special geometries based on homogeneous coset spaces. For non-BPS critical points (with non vanishing central charge) the (Bekenstein-Hawking) entropy formula is the same as for symmetric spaces, namely four times the square of the central charge evaluated at the critical point. For non homogeneous geometries the deviation from this formula is given in terms of geometrical data of special geometry in presence of a background symplectic charge vector.

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arXiv2006

Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy

In this paper we prove the theorem that there exists no 7--dimensional Lie group manifold G of weak G2 holonomy. We actually prove a stronger statement, namely that there exists no 7--dimensional Lie group with negative definite Ricci tensor Ric_{IJ}. This result rules out (supersymmetric and non--supersymmetric) Freund--Rubin solutions of M--theory of the form AdS_4\times G and compactifications with non--trivial 4--form fluxes of Englert type on an internal group manifold G. A particular class of such backgrounds which, by our arguments are excluded as bulk supergravity compactifications corresponds to the so called compactifications on twisted--tori, for which G has structure constants $τ^K{}_{IJ}$ with vanishing trace $τ^J{}_{IJ}=0$. On the other hand our result does not have bearing on warped compactifications of M--theory to four dimensions and/or to compactifications in the presence of localized sources (D--branes, orientifold planes and so forth). Henceforth our result singles out the latter compactifications as the preferred hunting grounds that need to be more systematically explored in relation with all compactification features involving twisted tori.

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arXiv2006

Spontaneously broken supergravity: Old and new facts

We report on some recent investigations of the structure of the four dimensional gauged supergravity Lagrangian which emerges from flux and Scherk-Schwarz compactifications in higher dimensions. Special attention is given to the gauge structure of M-theory compactified on a seven torus with 4-form and geometrical (spin connection) fluxes turned on. A class of vacua, with flat space-time and described by ``no-scale'' supergravity models, is analyzed.

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arXiv2005

Curvatures and potential of M-theory in D=4 with fluxes and twist

We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full $\rE_{7(7)}$ symmetry.

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arXiv2005

The Scherk-Schwarz mechanism as a flux compactification with internal torsion

The aim of this paper is to make progress in the understanding of the Scherk-Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can be directly identified with certain components of the four-form field-strength. Furthermore, we introduce a novel (four dimensional) approach to the study of dualities between flux/torsion compactifications of Type II/M-theory. This approach defines the action that duality should have on the background quantities, in order for the E7(7) invariance of the field equations and Bianchi identities to be restored also in the presence of fluxes/torsion. This analysis further implies the interpretation of the torsion flux as the T-dual of the NS three-form flux.

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