Hypermultiplet gaugings and supersymmetric solutions from 11D and massive IIA supergravity on $$\hbox {H}^{(p,q)}$$ H ( p , q ) spaces

Abstract

Supersymmetric AdS 4 , AdS 2 × 2 and asymptotically AdS 4 black hole solutions are studied in the context of non-minimal N = 2 supergravity models involving three vector multiplets (STU-model) and Abelian gaugings of the universal hypermultiplet moduli space. Such models correspond to consistent subsectors of the SO( p, q) and ISO( p, q) gauged maximal supergravities that arise from the reduction of 11D and massive IIA supergravity on H ( p,q) spaces down to four dimensions. A unified description of all the models is provided in terms of a square-root prepotential and the gauging of a duality-hidden symmetry pair of the universal hypermultiplet. Some aspects of M-theory and massive IIA holography are mentioned in passing. MotivationAsymptotically anti-de Sitter (AdS 4 ) black holes in minimal N = 2 gauged supergravity have recently been connected to a universal renormalisation group (RG) flow for a large class of three-dimensional N = 2 superconformal field theories (SCFTs) using holography [1]. The relevant (universal) AdS 4 black hole is static, extremal (thus T = 0) and of Reissner-Nordström (R-N) type with zero mass and a hyperbolic horizon 2 = H 2 [2]. The space-time metric takes the formwithand d 2 = dθ 2 + sinh 2 (θ )dφ 2 being the Riemann surface element on 2 = H 2 . The metric asymptotes an AdS 4 geometry with radius L AdS 4 when r → ∞, and conforms to a e-mail: adolfo.guarino@ulb.ac.be . This black hole is a solution of the equations of motion that follow from the cosmological Einstein-Maxwell LagrangianEndowing the Lagrangian (3) with N = 2 local supersymmetry requires the cosmological constant to be negative and also a mass term for the gravitini fields in the theory [3]. Furthermore, supersymmetry fixes the cosmological constant to V = −3L The AdS 4 black hole described above is gauge/gravity dual to a universal RG flow in field theory [1]. This is an RG flow across dimensions 1 from a three-dimensional N = 2 SCFT (dual to the asymptotic AdS 4 geometry) placed on H 2 and with a topological twist along the exact superconformal R-symmetry, to a one-dimensional superconformal quantum mechanics (dual to the AdS 2 factor of the black hole nearhorizon geometry). Such a universal RG flow admits various holographic embeddings in eleven-dimensional (11D) supergravity [6,7], the low-energy limit of M-theory, and tendimensional massive IIA supergravity [8]. Specific examples have been studied in the context of ABJM theory [9] and GJV/SYM-CS duality [10] (and its generalisation of [11]) involving reductions of M-theory and massive IIA strings on various compact spaces [1]. More concretely, when placing the SCFTs on S 1 × 2 , a counting of supersymmetric ground states using the topologically twisted index of [12] at large N was shown to exactly reproduce the Bekenstein-Hawking entropy associated with the AdS 4 black hole in (1), (2).

S-folds and (non-)supersymmetric Janus solutions

“…This is the same gauge group that arises from M-theory models based on reductions on H (7,1) and H (5,3) hyperbolic spaces, although in those cases, only electric vectors happen to enter the gauging [36]. For the type IIB model based on the reduction on R × S 5 , the SO(1, 1) factor in (2.28) is gauged by the magnetic graviphotonà 0 as it can be seen from (2.23).…”

“…denote a special Kähler (SK) and a quaternionic Kähler (QK) geometry. The scalar geometry in (2.9) involves a set of t A B (with t A A = 0 ) and t ABCD = t [ABCD] generators of E 7 (7) in the SL (8) basis (see appendix in [36] for conventions). The SK factor in (2.10) has associated generators given by…”

“…was investigated in [35,36] within the context of massive IIA and M-theory reductions on H (p,q) spaces. The scalar sector describes a coset geometry of the form…”

On the U(1)2-Invariant Sector of Dyonic Maximal Supergravity

“…Note: As this manuscript was being finalized, we received a paper by A. Guarino [26] where the truncation of dyonic gauged supergravity to N = 2 supergravity with U(1) 2 is also explained in detail. In particular, eqs.…”

“…(12), (14) of this paper is the same as eqs. (65)-(67) of [26]. The 70 scalar fields of D = 4 maximal supergravity parametrize the coset E 7(7) /SU (8).…”