Topological AdS/CFT

TL;DR

This paper constructs a holographic dual for a topologically twisted four-dimensional gauge theory using five-dimensional supergravity solutions, demonstrating metric independence and extending geometric structures.

Contribution

It introduces a new holographic dual for the Donaldson-Witten topological twist via asymptotically locally hyperbolic supergravity solutions, linking boundary topology with bulk geometry.

Findings

Holographic dual described by specific supergravity solutions

Partition function independence from boundary metric confirmed

Supersymmetric solutions satisfy first order differential equations

Abstract

We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged supergravity in five dimensions, with the four-manifold as conformal boundary. Under AdS/CFT, minus the logarithm of the partition function of the gauge theory is identified with the holographically renormalized supergravity action. We show that the latter is independent of the metric on the boundary four-manifold, as required for a topological theory. Supersymmetric solutions in the bulk satisfy first order differential equations for a twisted $Sp(1)$ structure, which extends the quaternionic Kahler structure that exists on any Riemannian four-manifold boundary. We comment on applications and extensions, including generalizations to other topological twists.