Dimensional Supergravity Theories Research Articles

Dual theory for maximally mathcal{N} extended flat supergravity

Maximally mathcal{N} extended 2 + 1 dimensional flat supergravity theories exist for a class of super-Poincaré algebras for arbitrary mathcal{N} . They have rich asymptotic structures and contain all interesting topological supergravity solutions in presence of non-trivial holonomy. For the asymptotic symmetry algebra being a suitable flat limit of the superconformal algebra, which is an infinite dimensional extension of two copies of Osp( mathcal{N} |2; R) group, we have found the 1 + 1 dimensional chiral WZW model as the dual quantum field theory that describes the dynamics of these solutions. In the Hamiltonian analysis, the reduced phase space resembles a flat super Liouville theory.

Gauged 2-form symmetries in 6D SCFTs coupled to gravity

We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

Unified non-metric (1, 0) tensor-Einstein supergravity theories and (4, 0) supergravity in six dimensions

The ultrashort unitary (4, 0) supermultiplet of 6d superconformal algebra OSp(8∗|8) reduces to the CPT-self conjugate supermultiplet of 4d superconformal algebra SU(2, 2|8) that represents the fields of maximal N = 8 supergravity. The graviton in the (4, 0) multiplet is described by a mixed tensor gauge field which can not be identified with the standard metric in 6d. Furthermore the (4, 0) supermultiplet can be obtained as a double copy of (2, 0) conformal supermultiplet whose interacting theories are non-Lagrangian. It had been suggested that an interacting non-metric (4, 0) supergravity theory might describe the strongly coupled phase of 5d maximal supergravity. In this paper we study the implications of the existence of an interacting non-metric (4, 0) supergravity in 6d. The (4, 0) theory can be truncated to non-metric (1, 0) supergravity coupled to 5,8 and 14 self-dual tensor multiplets that reduce to three of the unified magical supergravity theories in d = 5. This implies that the three infinite families of unified N = 2, 5d Maxwell-Einstein supergravity theories (MESGTs) plus two sporadic ones must have uplifts to unified non-metric (1, 0) tensor Einstein supergravity theories (TESGT) in d = 6. These theories have non-compact global symmetry groups under which all the self-dual tensor fields including the gravitensor transform irreducibly. Four of these theories are uplifts of the magical supergravity theories whose scalar manifolds are symmetric spaces. The scalar manifolds of the other unified theories are not homogeneous spaces. We also discuss the exceptional field theoretic formulations of non-metric unified (1, 0) tensor-Einstein supergravity theories and conclude with speculations concerning the existence of higher dimensional non-metric supergravity theories that reduce to the (4, 0) theory in d = 6.

String defects, supersymmetry and the Swampland

Recently, Kim, Shiu and Vafa proposed general consistency conditions for six dimensional supergravity theories with minimal supersymmetry coming from couplings to strings. We test them in explicit perturbative orientifold models in order to unravel the microscopic origin of these constraints. Based on the perturbative data, we conjecture the existence of null charges Q∙Q = 0 for any six-dimensional theory with at least one tensor multiplet, coupling to string defects of charge Q. We then include the new constraint to exclude some six-dimensional supersymmetric anomaly-free examples that have currently no string or F-theory realization. We also investigate the constraints from the couplings to string defects in case where supersymmetry is broken in tachyon free vacua, containing non-BPS configurations of brane supersymmetry breaking type, where the breaking is localized on antibranes. In this case, some conditions have naturally to be changed or relaxed whenever the string defects experience supersymmetry breaking, whereas the constraints are still valid if they are geometrically separated from the supersymmetry breaking source.

4D mathcal{N} = 1 Kaluza-Klein superspace

Motivated by recent efforts to encode 11D supergravity in 4D mathcal{N} = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D mathcal{N} = 1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the superfields necessary to encode the components of the higher dimensional vielbein, except for the purely internal sector, in a universal way that depends only on the internal dimension n. In contrast, the mathcal{N} = 1 superfield content of the internal sector of the metric is expected to be highly case dependent and involve covariant matter superfields, with additional hidden higher dimensional Lorentz and supersymmetry transformations realized in a non-linear manner.

E11 must be a symmetry of strings and branes

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in five and eleven dimensions and find the dynamical equations it predicts at low levels. Restricting these results to contain only the usual fields of supergravity and the generalised space-time to be the usual space-time we find the equations of motion of the five and eleven dimensional maximal supergravity theories. Since this non-linear realisation contains effects that are beyond the supergravity approximation and are thought to be present in an underlying theory we conclude that the low energy effective action of string and branes must possess an E11 symmetry.

Supersymmetry Constraints and String Theory on K3

We study supervertices in six dimensional (2,0) supergravity theories, and derive supersymmetry non-renormalization conditions on the 4- and 6-derivative four-point couplings of tensor multiplets. As an application, we obtain exact non-perturbative results of such effective couplings in type IIB string theory compactified on K3 surface, extending previous work on type II/heterotic duality. The weak coupling limit thereof, in particular, gives certain integrated four-point functions of half-BPS operators in the nonlinear sigma model on K3 surface, that depend nontrivially on the moduli, and capture worldsheet instanton contributions.

Power-law cosmologies in minimal and maximal gauged supergravity

In this paper we search for accelerating power-law solutions and ekpyrotic solutions within minimal and maximal four dimensional supergravity theories. We focus on the STU model for N = 1 and on the new CSO(p, q, r) theories, which were recently obtained exploiting electromagnetic duality, for N = 8. In the minimal case we find some new ekpyrotic solutions, while in the maximal case we find some new generic power-law solutions. We do not find any new accelerating solutions for these models.

D-geometries revisited

Abstract We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N > 2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N = 2 special Kähler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

Extremal multicenter black holes: nilpotent orbits and Tits Satake universality classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.

Degenerate rotating black holes, chiral CFTs and Fermi surfaces I — Analytic results for quasinormal modes

In this work we discuss charged rotating black holes in $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of $\mathcal{N}=4$ SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using the asymptotic matching expansion method applied to a Heun equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the supersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1+1 CFT, which is consistent with the conjectured field-theoretic dual. In addition, some of the modes can be found analytically.

Spectrum generating conformal and quasiconformal U-duality groups, supergravity and spherical vectors

After reviewing the algebraic structures that underlie the geometries of N = 2 Maxwell-Einstein supergravity theories (MESGT) with symmetric scalar manifolds in five and four dimensions, we give a unified realization of their three dimensional U-duality groups as spectrum generating quasiconformal groups. They are F 4(4),E 6(2),E 7(−5),E 8(−24) and SO(n+2, 4). Our formulation is covariant with respect to U-duality symmetry groups of corresponding five dimensional supergravity theories, which are SL(3, $ \mathbb{R} $ ), SL(3, $ \mathbb{C} $ ), SU*(6), E 6(−26) and SO(n − 1, 1) × SO(1, 1), respectively. We determine the spherical vectors of quasiconformal realizations of all these groups twisted by a unitary character ν. We present their quadratic Casimir operators and determine their values in terms of ν and the number n V of vector fields of the respective 5D supergravity. For ν = −(n V + 2) + iρ the quasiconformal action induces unitary representations belonging to the principal series. For special discrete values of ν it leads to unitary representations belonging to the quaternionic discrete series. Our results lay the algebraic groundwork for constructing explicitly the quaternionic discrete series unitary representations. For rank 2 cases, SU(2, 1) and G 2(2), corresponding to simple N = 2 supergravity in four and five dimensions, respectively, this program was carried out in arXiv:0707.1669 and applied to quantum attractor flows.

Quasiconformal Realizations of $E_{6(6)}, E_{7(7)}, E_{8(8)}$ and $SO(n+3,m+3), N=4 and N>4$ Supergravity and Spherical Vectors

After reviewing the underlying algebraic structures we give a unified realization of split exceptional groups F_{4(4)},E_{6(6)}, E_{7(7)}, E_{8(8)} and of SO(n+3,m+3) as groups that is covariant with respect to their (Lorentz) subgroups SL(3,R), SL(3,R)XSL(3,R), SL(6,R), E_{6(6)} and SO(n,m)XSO(1,1), respectively. We determine the spherical vectors of realizations of all these groups twisted by a unitary character $\nu$. We also give their quadratic Casimir operators and determine their values in terms of $\nu$ and the dimension $n_V$ of the underlying Jordan algebras. For $\nu= -(n_V+2)+i\rho$ the action induces unitary representations on the space of square integrable functions in $(2n_V+3)$ variables, that belong to the principle series. For special discrete values of $\nu$ the action leads to unitary representations belonging to the discrete series and their continuations. The manifolds that correspond to quasiconformal compactifications of the respective $(2n_V+3)$ dimensional spaces are also given. We discuss the relevance of our results to N=8 supergravity and to N=4 Maxwell-Einstein supergravity theories and, in particular, to the proposal that three and four dimensional U-duality groups act as spectrum generating and conformal groups of the corresponding four and five dimensional supergravity theories, respectively.

First-order attractor flow equations for supersymmetric black rings inN= 2,D= 5 supergravity

In this paper we investigate the attractor mechanism in the five dimensional low energy supergravity theory corresponding to M-theory compactified on a Calabi-Yau threefold $CY_3$. Using very special geometry, we derive the general first-order attractor flow equations for BPS and non-BPS solutions in five-dimensional Gibbons-Hawking spaces. Especially, considering the supersymmetric solution, we obtain the first-order flow equations for supersymmetric (multi)black rings. We also solve the flow equations and discuss some properties of the solutions of flow equations.

Moduli stabilization in meta-stable heterotic supergravity vacua

We revisit the issue of moduli stabilization in a class of N=1 four dimensional supergravity theories which are low energy descriptions of standard perturbative heterotic string vacua compactified on Calabi-Yau spaces. In particular, we show how it is possible to stabilize the universal dilaton and Kahler moduli in a de Sitter/Minkowski vacuum with low energy supersymmetry breaking by means of non-perturbative gauge dynamics, including recent results by Intriligator, Seiberg and Shih. The non-SUSY vacua are meta-stable but sufficiently long-lived.

Massive super-Yang–Mills quantum mechanics: Classification and the relation to supermembrane

We classify the supersymmetric mass deformations of all the super-Yang–Mills quantum mechanics, which are obtained by dimensional reductions of minimal super-Yang–Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu–Goto action for a p-brane, including time dependent backgrounds.

Integrable Models of (1+1)-Dimensional Dilaton Gravity Coupled to Scalar Matter

A class of explicitly integrable models of 1+1 dimensional dilaton gravity coupled to scalar fields is described in some detail. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and momentum constraints. The general solution of the equations and constraints in terms of chiral moduli fields is explicitly constructed and some extensions of the basic integrable model are briefly discussed. These models may be related to high dimensional supergravity theories but here they are mostly considered independently of such interpretations. A brief review of other integrable models of two-dimensional dilaton gravity is also given.

Moduli potentials in string compactifications with fluxes: Mapping the discretuum

We find de Sitter and flat space solutions with all moduli stabilized in four dimensional supergravity theories derived from the heterotic and type II string theories, and explain how all the previously known obstacles to finding such solutions can be removed. Further, we argue that if the compact manifold allows a large enough space of discrete topological choices then it is possible to tune the parameters of the four dimensional supergravity such that a hierarchy is created and the solutions lie in the outer region of moduli space in which the compact volume is large in string units, the string coupling is weak, and string perturbation theory is valid. We show that at least two light chiral superfields are required for this scenario to work, however, one field is sufficient to obtain a minimum with an acceptably small and negative cosmological constant. We discuss cosmological issues of the scenario and the possible role of anthropic considerations in choosing the vacuum of the theory. We conclude that the most likely stable vacuua are in or near the central region of moduli space where string perturbation theory is not strictly valid, and that anthropic considerations cannot help much in choosing a vacuum.

No-scaleD=5 supergravity from Scherk-Schwarz reduction ofD=6 theories

We perform a generalized dimensional reduction of six dimensional supergravity theories to five dimensions. We consider the minimal $(2,0)$ and the maximal $(4,4)$ theories. In each case the reduction allows us to obtain gauged supergravities of no-scale type in dimension five with gauge groups that escape previous classifications. In the minimal case, the geometric data of the reduced theory correspond to particular cases of the D=5 real special geometry. In the maximal case we find a four parameter solution which allows partial breaking of supersymmetry.

E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories

In view of the newly conjectured Kac-Moody symmetries of supergravity theories placed in eleven and ten dimensions, the relation between these symmetry groups and possible compactifications are examined. In particular, we identify the relevant group cosets that parametrise the vacuum solutions of AdS x S type.