ADS₄/CFT₃ Holography from four-dimensional gauged supergravity

Abstract

We study holographic RG flows from N = 3 and N = 4 gauged supergravities in four dimensions. The scalar manifold of N = 3 gauged supergravity is in the form of the coset space G/H = SU(3, n)/SU(3) × SU(n) × U(1). Possible gauge groups, in this study, are given by SO(3) × SO(3), SO(3, 1), SO(2, 2), SO(2, 1) × SO(2, 2), and SL(3, R). We then study N = 4 gauged supergravity from type II compactification on T⁶/Z₂ × Z₂ with non-semisimple gaugings. The scalar manifold of N = 4 gauged supergravity is in the form of SL(2, R)/SO(2) × SO(6, n)/SO(6) × SO(n) coset. The gauge group arising from non-geometric compactification of type IIB is ISO(3) × ISO(3), which is embedded in SO(6,6) via the SO(3,3) × SO(3,3) subgroup. We also consider N=4 gauged supergravity from type IIB GKP (Giddings-Kachru-Polchinski) compactification. We similarly study non-semisimple ISO(3) ⋉ U(1) ⁶ gauge group arising from type IIA geometric compactification. For semisimple gaugings, we consider SO(4) × SO(4), SO(3, 1) × SO(3, 1), SO(2, 2) × SO(2, 2), SO(4) × SO(3, 1), SO(4) × SO(2, 2), and SO(3, 1) × SO(2, 2) gauge groups. A number of supersymmetric AdS₄ critical points for each gauge group are found. We give RG flow solutions interpolating between these critical points together with possible flows to non-conformal theories, in each gauge group. We also give examples of Janus solutions for N = 4 gauged supergravity obtained from type IIB non-geometric compactification.