arXiv subjects
Publications and source records attributed to Mario Trigiante.
We find regular axionic Euclidean wormhole solutions in Type IIB string theory compactified on $\text{AdS}_5\times \text{S}^5/\mathbb{Z}_k$. AdS/CFT enables a precise derivation of the axion content of the Euclidean theory, placing the string theory embedding of the wormholes on firm footing. This further sharpens the paradox posed by these solutions.
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of SL_2(R)^4 acting on the fourth tensor power of the natural 2-dimensional SL_2(R)-module. This makes it possible to classify all stationary solutions of the so-called STU-supergravity model.
The complete classification of the nilpotent orbits of ${\rm SO}(2,2)^2$ in the representation ${\bf (2,2,2,2)}$, achieved in \cite{Dietrich:2016ojx}, is applied to the study of multi-center, asymptotically flat, extremal black hole solutions to the STU model. These real orbits provide an intrinsic characterization of regular single-center solutions, which is invariant with respect to the action of the global symmetry group ${\rm SO}(4,4)$, underlying the stationary solutions of the model, and provide stringent regularity constraints on multi-centered solutions. The known \emph{almost-BPS} and \emph{composite non-BPS} solutions are revisited in this setting. We systematically provide, for the relevant ${\rm SO}(2,2)^2$-nilpotent orbits of the global Noether charge matrix, regular representatives thereof. This analysis unveils a composition law of the orbits according to which those containing regular multi-centered solutions can be obtained as combinations of specific single-center orbits defining the constituent black holes. Some of the ${\rm SO}(2,2)^2$-orbits of the total Noether charge matrix are characterized as "intrinsically singular" in that they cannot contain any regular solution.
We perform a systematic search for anti-de Sitter vacua of maximal supergravity with N>2 residual supersymmetries. We find that maximal supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively. They are embedded, for the different values of an angular parameter, in the $ω$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua disappear in the limit when $ω$ tends to zero. We determine the mass spectra and the AdS-supermultiplet structure. These appear to be the first and only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8 vacua of the SO(8)-gauged models. We also prove on general grounds that no such vacua can exist for 4<N<8.
The c-map of four dimensional non-linear theories of electromagnetism is considered both in the rigid case and in its coupling to gravity. In this way theories with antisymmetric tensors and scalars are obtained, and the three non-linear representations of N=2 supersymmetry partially broken to N=1 related. The manifest $\mathrm{Sp}(2n)$ and $\mathrm{U}(n)$ covariance of these theories in their multifield extensions is also exhibited.
The multi-vector generalization of a rigid, partially-broken $\mathcal{N}=2$ supersymmetric theory is presented as a rigid limit of a suitable gauged $\mathcal{N}=2$ supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models from $\mathcal{N}=2$ supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory will be elucidated, such as the presence of a traceless ${\rm SU}(2)$- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of "superspace non-locality" which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic $\mathcal{N}=2$ model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.
We construct a general Lagrangian, quadratic in the field strengths of $n$ abelian gauge fields, which interpolates between BI actions of n abelian vectors and actions, quadratic in the vector field-strengths, describing Maxwell fields coupled to non-dynamical scalars, in which the electric-magnetic duality symmetry is manifest. Depending on the choice of the parameters in the Lagrangian, the resulting BI actions may be inequivalent, exhibiting different duality groups. In particular we find, in our general setting, for different choices of the parameters, a ${\rm U}(n)$-invariant BI action, possibly related to the one in \cite{Aschieri:2008ns}, as well as the recently found $\mathcal{N}=2$ supersymmetric BI action \cite{Ferrara:2014oka}.
We study the partial breaking of $N=2$ rigid supersymmetry for a generic rigid special geometry of $n$ abelian vector multiplets in the presence of Fayet-Iliopoulos terms induced by the Hyper-Kähler momentum map. By exhibiting the symplectic structure of the problem we give invariant conditions for the breaking to occur, which rely on a quartic invariant of the Fayet-Iliopoulos charges as well as on a modification of the $N=2$ rigid symmetry algebra by a vector central charge.
We consider N=2 supergravity theories that have the same spectrum as the R+R^2 supergravity, as predicted from the off-shell counting of degrees of freedom. These theories describe standard N=2 supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with N=2 unbroken supersymmetry. The gauge symmetry, being non-compact, is always broken. $α$-deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with $α=1/3$ and $2/3$. The $α=1$ potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non-compact quaternionic-K{ä}hler cosets.
With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting global symmetry orbits (duality orbits) of non-extremal solutions to those of extremal black holes. We focus our attention on a generic representative of these orbits, providing its explicit description in terms of D=4 fields. As a byproduct, using a new characterization of the angular momentum in terms of quantities intrinsic to the geometry of the D=3 effective model, we are able to prove on general grounds its invariance, as a function of the boundary data, under the D=4 global symmetry. In the extremal under-rotating limit it becomes moduli-independent. We also discuss the issue of the fifth parameter characterizing the four-dimensional seed solution, showing that it can be generated by a transformation in the global symmetry group which is manifest in the D=3 effective description.
In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M(ϕ), related to the coupling of scalars ϕ to vector field-strengths. In particular, this matrix enters the twisted self-duality condition for 2-form field strengths in the symplectic formulation of generalized Maxwell equations in the presence of scalar fields. In this investigation, we compute several properties of this matrix in relation to the attractor mechanism of extremal (asymptotically flat) black holes. At the attractor points with no flat directions (as in the N = 2 BPS case), this matrix enjoys a universal form in terms of the dyonic charge vector Q and the invariants of the corresponding symplectic representation RQ of the duality group G, whenever the scalar manifold is a symmetric space with G simple and non-degenerate of type E7. At attractors with flat directions, M still depends on flat directions, but not MQ, defining the so-called Freudenthal dual of Q itself. This allows for a universal expression of the symplectic vector field strengths in terms of Q, in the near-horizon Bertotti-Robinson black hole geometry.
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow to do so is called expansion of Lie algebras, and has been recently used in different physical applications - particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by the some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows to check explicitly all our theoretical results is also provided.
We consider non-extremal, stationary, axion-dilaton solutions to ungauged symmetric supergravity models, obtained by Harrison transformations of the non-extremal Kerr solution. We define a general algebraic procedure, which can be viewed as an Inonu-Wigner contraction of the Noether charge matrix associated with the effective D=3 sigma-model description of the solution, yielding, through different singular limits, the known BPS and non-BPS extremal black holes (which include the under-rotating non-BPS one). The non-extremal black hole can thus be thought of as "interpolating" among these limit-solutions. The algebraic procedure that we define generalizes the known Rasheed-Larsen limit which yielded, in the Kaluza-Klein theory, the first instance of under-rotating extremal solution. As an example of our general result, we discuss in detail the non-extremal solution in the T^3-model, with either (q_0, p^1) or (p^0, q_1) charges switched on, and its singular limits. Such solutions, computed in D=3 through the solution-generating technique, is completely described in terms of D=4 fields, which include the fully integrated vector fields.
We classify the enhanced helicity symmetry of the Ehlers group to extended supergravity theories in any dimension. The vanishing character of the pseudo-Riemannian cosets occurring in this analysis is explained in terms of Poincaré duality. The latter resides in the nature of regularly embedded quotient subgroups which are non-compact rank preserving.
In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory associated with the effective two-dimensional sigma-model action describing the axisymmetric solutions. We write the general form of the two functions S_m defining the first-order equations for the fields. It is invariant under the global symmetry group G_(3) of the sigma-model. We also discuss the general properties of the solutions with respect to these global symmetries, showing that they can be encoded in two constant matrices belonging to the Lie algebra of G_(3), one being the Noether matrix of the sigma model, while the other is non-zero only for rotating solutions. These two matrices allow a G_(3)-invariant characterization of the rotational properties of the solution and of the extremality condition. We also comment on extremal, under-rotating solutions from this point of view.
We explain when the first-order Hamilton-Jacobi equations for black holes (and domain walls) in (gauged) supergravity, reduce to the usual first-order equations derived from a fake superpotential. This turns out to be equivalent to the vanishing of a newly found constant of motion and we illustrate this with various examples. We show that fake supersymmetry is a necessary condition for having physically sensible extremal black hole solutions. We furthermore observe that small black holes become scaling solutions near the horizon. When combined with fake supersymmetry, this leads to a precise extension of the attractor mechanism to small black holes: The attractor solution is such that the scalars move on specific curves, determined by the black hole charges, that are purely geodesic, although there is a non-zero potential.
In this paper we consider the problem of classification of nilpotent orbits for the pseudo-quaternionic coset manifolds U/H* obtained in the time-like dimensional reduction of N = 2 supergravity models based on homogeneous symmetric special geometries. Within the D=3 approach this classification amounts to a classification of regular and singular extremal black hole solutions of supergravity. We show that the pattern of such orbits is a universal property depending only on the Tits-Satake universality class of the considered model, the number of such classes being five. We present a new algorithm for the classification and construction of the nilpotent orbits for each universality class which is based on an essential use of the Weyl group W of the Tits Satake subalgebra U_{TS} of U and on a certain subgroup W_H thereof. The splitting of orbits of the full group Uinto suborbits with respect to the stability subgroup H* is shown to be governed by the structure of the discrete coset W/W_H. For the case of the universality class SO(4,5) /[SO(2,3) x SO(2,2)] we derive the complete list of nilpotent orbits which happens to contain 37 elements. We also show how the universal orbits are regularly embedded in all the members of the class that are infinite in number. As a matter of check we apply our new algorithm also to the Tits Satake class G_(2,2)/[SL(2)x SL(2)] confirming the previously obtained result encompassing 7 nilpotent orbits. Perspectives for future developments based on the obtained results are outlined.
We construct the general four-dimensional N=2 supergravity theory coupled to vector and vector-tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same supermultiplets as the antisymmetric tensors, as well as the scalar fields dual to the tensors themselves. Gauge symmetries also involving these additional fields guarantee the correct counting of the physical degrees of freedom.