AdS spacetimes from wrapped D3-branes

TL;DR

The authors develop a G-structure framework to classify $AdS$ spacetimes in type IIB supergravity with $F_5$ flux arising from wrapped D3-branes on calibrated cycles. By treating wrapped-brane geometries as seeds and imposing $AdS$-limits, they derive several $AdS_2$ and $AdS_3$ classes associated with associative, SLAG-3, and Kähler-2 cycles in manifolds of $G_2$, SU(3), SU(4) holonomy, and they verify two known AdS solutions satisfy the torsion conditions. They also construct special-holonomy metrics (some singular) that carry the appropriate calibrated cycles and discuss analytic continuations to BPS bubble geometries with distinct supersymmetries and R-symmetries, including a new 1/8-BPS class with $ ext{R}$-symmetry $SU(2)$. The work includes explicit checks against gauged supergravity solutions and proposes an interpolating ansatz suggesting smooth flows between special holonomy and AdS fixed points. Overall, the results extend the catalog of supersymmetric AdS solutions via wrapped-brane G-structures and illuminate their holographic duals.

Abstract

We derive a geometrical characterisation of a large class of AdS_3 and AdS_2 supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux using G-structures. These are obtained as special cases of a class of supersymmetric spacetimes with an $\mathbb{R}^{1,1}$ or $\mathbb{R}$ (time) factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles, respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show how two explicit AdS solutions, previously constructed in gauged supergravity, satisfy our more general G-structure conditions. For each explicit solution we also derive a special holonomy metric which, although singular, has an appropriate calibrated cycle. After analytic continuation, some of the classes of AdS spacetimes give rise to known classes of BPS bubble solutions with $\mathbb{R}\times SO(4)\times SO(4)$, $\mathbb{R}\times SO(4)\times U(1)$, and $\mathbb{R}\times SO(4)$ symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with $\mathbb{R}\times SU(2)$ symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-branes wrapped on associative three-cycles.