Maximally supersymmetric AdS solutions and their moduli spaces
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Springer
Received: December 29, 2017 Accepted: February 20, 2018 Published: March 6, 2018
Maximally supersymmetric AdS solutions and their moduli spaces
´ Centre de Physique Th´eorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France b Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, U.K. c Fachbereich Physik der Universit¨ at Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany d Zentrum f¨ ur Mathematische Physik, Universit¨ at Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
a
E-mail: [email protected], [email protected], [email protected] Abstract: We study maximally supersymmetric AdSD solutions of gauged supergravities in dimensions D ≥ 4. We show that such solutions can only exist if the gauge group after spontaneous symmetry breaking is a product of two reductive groups HR ×Hmat , where HR is uniquely determined by the dimension D and the number of supersymmetries N while Hmat is unconstrained. This resembles the structure of the global symmetry groups of the holographically dual SCFTs, where HR is interpreted as the R-symmetry and Hmat as the flavor symmetry. Moreover, we discuss possible supersymmetry preserving continuous deformations, which correspond to the conformal manifolds of the dual SCFTs. Under the assumption that the scalar manifold of the supergravity is a symmetric space we derive general group theoretical conditions on these moduli. Using these results we determine the AdS solutions of all gauged supergravities with more than 16 real supercharges. We find that almost all of them do not have supersymmetry preserving deformations with the only exception being the maximal supergravity in five dimensions with a moduli space given by SU(1, 1)/U(1). Furthermore, we determine the AdS solutions of four-dimensional N = 3 supergravities and show that they similarly do not admit supersymmetric moduli. Keywords: Extended Supersymmetry, Supergravity Models, AdS-CFT Correspondence ArXiv ePrint: 1711.06180
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)019
JHEP03(2018)019
Severin L¨ ust,a Philipp R¨ uterb and Jan Louisc,d
Contents 1 Introduction
1 4 4 8 13
3 AdS solutions and their moduli spaces 3.1 The gauge group of AdS solutions 3.2 The moduli space
16 16 20
4 AdS solutions with q > 16 supercharges 4.1 Four-dimensional AdS solutions 4.2 Five-dimensional AdS solutions 4.3 Seven-dimensional AdS solutions
28 31 33 35
5 AdS solutions in four-dimensional N = 3 supergravity
36
6 Conclusions
38
7 Conventions and notations
39
8 Supersymmetry variations 8.1 Supersymmetry variations 8.2 The general Lagrangian 8.3 Killing vectors and moment maps 8.4 Supersymmetry variations in various dimensions
42 43 44 45 47
g 9 Properties of the gauged R-symmetry group HR
50
10 Variation of the vielbeins
51
11 Symmetric moduli spaces
55
1
Introduction
Anti-de Sitter backgrounds of supergravity theories play an important role in the context of the AdS/CFT corresp
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