Gauged supergravity from the Lunin-Maldacena background
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Springer
Received: July 11, Revised: December 19, Accepted: January 6, Published: January 29,
2019 2019 2020 2020
James T. Liu and Brian McPeak Leinweber Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI 48109-1040, U.S.A.
E-mail: [email protected], [email protected] Abstract: We show how to expand the Lunin-Maldacena solution to the full bosonic sector of gauged N = 2 supergravity. In particular, we construct a consistent truncation of IIB supergravity on a β-deformed AdS5 × S 5 background retaining a dynamical metric and graviphoton in five dimensions. We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution. Keywords: AdS-CFT Correspondence, Supergravity Models ArXiv ePrint: 1905.06861
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)177
JHEP01(2020)177
Gauged supergravity from the Lunin-Maldacena background
Contents 1
2 Reduction to N = 2 gauged supergravity 2.1 The reduction ansatz 2.2 Verification of the ansatz
2 3 5
3 Discussion
6
A Type IIB supergravity conventions
8
1
Introduction
It has long been known that N = 4 super Yang-Mills (SYM) admits two exactly marginal deformations which break supersymmetry to N = 1 [1]. These are the β deformations and enter in the Lagrangian through Tr (Φ1 Φ2 Φ3 + Φ1 Φ3 Φ2 ) and Tr Φ31 + Φ32 + Φ33 terms in the superpotential. From an AdS/CFT point of view, these deformations should admit bulk duals which are solutions of type IIB supergravity on a correspondingly deformed AdS 5 ×S 5 background. However the problem of determining these solutions is highly non-trivial. Marginal deformations in the field theory are generated by turning on massless scalars in the AdS dual that couple to operators with conformal dimension ∆ = 4. For N = 4 SYM, the dual is given by IIB supergravity on AdS5 × S 5 , and its Kaluza-Klein (KK) spectrum has been extensively studied following the initial work of [2, 3]. At the lowest KK level, the 42 scalars of N = 8 gauged supergravity transform as 200 +(10+10)+(1+1) of SU(4)R , with corresponding dimensions 2, 3 and 4. The latter complex scalar is identified as the IIB axi-dilaton, which is dual to the complexified gauge coupling, and generates an exactly marginal deformation of N = 4 SYM. Additional massless scalars arise in the 45 + 45 representation at the first excited KK level, and in the 105 representation at the second excited level. Of course, not all of these generate exactly marginal deformations, and the scalars dual to the β deformation are fully contained in the 45 + 45 representation that arises as a KK excitation of the complex two-form potential of IIB supergravity. The supergravity deformations resulting from these scalars were examined up to second order in [4], and subsequently a full non-linear construction of the β deformation corresponding to Tr (Φ1 Φ2 Φ3 + Φ1 Φ3
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