AdS Solutions Through Transgression

TL;DR

The work expands the landscape of supersymmetric AdS solutions by exploiting transgression terms to activate fluxes in both type IIB $AdS_{3}$ backgrounds and $D=11$ $AdS_{2}$ backgrounds, while preserving the AdS factors and a common Kähler-leaf structure. It develops a unifying framework in which the internal spaces are foliated Kähler manifolds whose geometry is governed by a modified master equation that incorporates flux contributions. The authors construct infinite families of explicit solutions, derive central charges for several $AdS_{3}$ Type IIB cases, and elucidate how T-duality and S-duality connect these solutions to NS-flux-dominated frames, including the well-known $AdS_{3}\times S^{3}\times S^{3}\times S^{1}$ geometry. The results significantly broaden the holographic examples with $(0,2)$ SCFT duals and two-supercharge quantum-mechanical systems, while offering concrete avenues for flux quantisation analyses and potential worldsheet CFT descriptions.

Abstract

We present new classes of explicit supersymmetric AdS_3 solutions of type IIB supergravity with non-vanishing five-form flux and AdS_2 solutions of D=11 supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general solutions makes essential use of the Chern-Simons or "transgression" terms in the Bianchi identity or the equation of motion of the field strengths in the supergravity theories. We construct infinite new classes of explicit examples and for some of the type IIB solutions determine the central charge of the dual SCFTs. The type IIB solutions with non-vanishing three-form flux that we construct include a two-torus, and after two T-dualities and an S-duality, we obtain new AdS_3 solutions with only the NS fields being non-trivial.