P. Fre

N=2 supergravity and N=2 superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map

Abstract The general form of N = 2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete Lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Lagrangians for rigid theories are also written in this general setting and the connection with local theories elucidated. The derivation of these results using geometrical techniques is briefly summarized.

3D superconformal theories from Sasakian seven-manifolds: New non-trivial evidences for AdS4/CFT3

Abstract In this paper we discuss candidate superconformal N =2 gauge theories that realize the AdS/CFT correspondence with M-theory compactified on the homogeneous Sasakian 7 -manifolds M 7 that were classified long ago. In particular we focus on the two cases M 7 =Q 1,1,1 and M 7 =M 1,1,1 , for the latter the Kaluza–Klein spectrum being completely known. We show how the toric description of M 7 suggests the gauge group and the supersingleton fields. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5 -branes wrapped on supersymmetric 5 -cycles and are charged with respect to the Betti multiplets. The entire Kaluza–Klein spectrum of short multiplets agrees with these dimensions. Furthermore, the metric cone over the Sasakian manifold is a conifold algebraically embedded in some C p . The ring of chiral primary fields is defined as the coordinate ring of C p modded by the ideal generated by the embedding equations; this ideal has a nice characterization by means of representation theory. The entire Kaluza–Klein spectrum is explained in terms of these vanishing relations. We give the superfield interpretation of all short multiplets and we point out the existence of many long multiplets with rational protected dimensions, whose presence and pattern seem to be universal in all compactifications.

General matter coupled N=2 supergravity

Abstract The general form of N = 2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows us to cover theories difficult to formulate within a superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting N = 2 supergravity as low energy limit.

R-R SCALARS, U-DUALITY AND SOLVABLE LIE ALGEBRAS

We consider the group theoretical properties of R-R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra Gs ⊂ U of the U-duality algebra that generates the scalar manifold of the theory: exp[Gs] = U/H. Peccei-Quinn symmetries are naturally related with the maximal abelian ideal A ⊂ Gs of the solvable Lie algebra. The solvable algebras of maximal rank occurring in maximal supergravities in diverse dimensions are described in some detail. A particular example of a solvable Lie algebra is a rank one, 2(h2,1+2)-dimensional algebra displayed by the classical quatemionic spaces that are obtained via the c-map from the special Kahlerian moduli spaces of Calabi-Yau threefolds.

N = 8 gaugings revisited: an exhaustive classification

In this paper we reconsider, for N = 8 supergravity, the problem of gauging the most general electric subgroup. We show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding Ggauge → SL(8, R) ⊂ E7(7). The complete set of solutions to this equation contains 36 parameters. Modding by the action of SL(8, R) conjugations that yield equivalent theories all continuous parameters are eliminated except for an overall coupling constant and we obtain a discrete set of orbits. This set is in one-to-one correspondence with 36 Lie subalgebras of SL(8, R), corresponding to all possible real forms of the SO(8) Lie algebra plus a set of contractions thereof. By means of our analysis we establish the theorem that the N = 8 gaugings constructed by Hull in the middle eighties constitute the exhaustive set of models. As a corollary we show that there exists a unique seven-dimensional abelian gauging. The corresponding abelian algebra is not contained in the maximal abelian ideal of the solvable Lie algebra generating the scalar manifold E7(7)/SU(8)

SU(3) x SU(2) x U(1) FROM D = 11 SUPERGRAVITY

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ⊗ SU(2) ⊗ U(1) as a symmetry of the internal space M7. These solutions lead, in dimensional reduction, to SU(3) ⊗ SU(2) ⊗ U(1) gauge fields. In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ⊗ U(1) ⊗ U(1) of M7 in SU(3) ⊗ SU(2) ⊗ U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl Fαβγδ ≠ 0. It breaks all sypersymmetries.

Stable de Sitter vacua from N=2 supergravity

We find extrema of the potential of matter couplings to = 2 supergravity that define de Sitter vacua and no tachyonic modes. There are three essential ingredients in our construction, namely non-Abelian non-compact gaugings, de Roo–Wagemans rotation angles and Fayet–Iliopoulos terms.

Solvable Lie algebras in type IIA, type IIB and M-theories

Abstract We study some applications of solvable Lie algebras in type IIA, type IIB and M-theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent ideals (translational symmetries of the scalar manifolds) in arbitrary D dimensions. These are seen to be related, using Dynkin diagram techniques, to one-form counting in D + 1 dimensions. A recipe for gauging isometries in this framework is also presented. In particular, we list the gauge groups both for compact and translational isometries. The former agree with some results already existing in gauged supergravity. The latter should be possibly related to the study of partial supersymmetry breaking, as suggested by a similar role played by solvable Lie algebras in N = 2 gauged supergravity.

N = 2 matter coupled supergravity from compactification on a coset G/H possessing an additional killing vector

Abstract The seven-dimensional coset manifolds SU(2) ⊗ SU(2) ⊗ SU(2) U(1) ⊗ U(1) = G H are characterized by three integer numbers p , q , r describing the embedding of the H = U (1) ⊗ U (1) subgroup in SU (2) ⊗ SU (2) ⊗ SU (2). On each coset one can construct on Einstein G-invariant metric leading to a solution of d = 11 supergravity. In general the holonomy group is SO(7), but for p = q = r = 1 it is SU(3) which allows the existence of two covariantly constant spinors η A . These latter are actually constant and k α = ϵ AB η A τ α η B is an additionalaa Killing vector which extends the symmetry of G/H to G ′ = SU (2)⊗ SU (2) ⊗ SU (2) ⊗ SO (2). N = 2 supersymmetry survives in this case and we have an Osp ( 4 2 ) ⊗ SU(2) ⊗ SU(2) ⊗ SU(2) invariant solution which yields, in four dimensions, N = 2 supergravity coupled to at least the N = 2 SU (2) ⊗ SU (2) ⊗ SU (2) vector multiplet.

Spontaneous N = 2 → N = 1 local supersymmetry breaking with surviving compact gauge groups

Abstract Generic partial supersymmetry breaking of N = 2 supergravity with zero vacuum energy and with surviving unbroken arbitrary gauge groups is exhibited. Specific examples are given.