3D Supergravity from wrapped D3-branes

TL;DR

The paper provides a unified framework linking AdS$3$ solutions from wrapped D3-branes to three-dimensional gauged supergravities via consistent KK reductions. It derives the $T$ tensor as the gravity-side analogue of $c$-extremization, enabling exact central charges and R-symmetries to be read off from 3D vacua, and it explores both generic and less generic reductions on various internal manifolds including Sasaki–Einstein and Calabi–Yau products. It also studies null-warped AdS$3$ geometries within these 3D theories, identifying conditions under which Schrödinger-like spacetimes with dynamical exponent $z$ arise and how they relate to higher-dimensional string constructions. The results illuminate how twisted compactifications of 4d and 1d SCFTs map to 3d gauged supergravity vacua, providing concrete tools for holographic $c$-extremization and potential connections to non-relativistic holography.

Abstract

AdS_3 solutions dual to N = (0,2) SCFTs arise when D3-branes wrap Kahler two-cycles in manifolds with SU(4) holonomy. Here we review known AdS_3 solutions and identify the corresponding three-dimensional gauged supergravities, solutions of which uplift to type IIB supergravity. In particular, we discuss gauged supergravities dual to twisted compactifications on Riemann surfaces of both N=4 SYM and N =1 SCFTs with Sasaki-Einstein duals. We check in each case that c-extremization gives the exact central charge and R symmetry. For completeness, we also study AdS_3 solutions from intersecting D3-branes, generalise recent KK reductions of Detournay & Guica and identify the underlying gauged supergravities. Finally, we discuss examples of null-warped AdS_3 solutions to three-dimensional gauged supergravity, all of which embed in string theory.