AdS Membranes Wrapped on Surfaces of Arbitrary Genus

TL;DR

This paper constructs and analyzes supergravity solutions for M2-branes wrapped on arbitrary genus surfaces, exploring their stability, holographic duals, and extensions to other branes.

Contribution

It introduces new supergravity solutions for M2-branes on arbitrary genus surfaces and examines their stability and holographic implications.

Findings

Higher genus branes are likely unstable.

Holographic duals suggest different phases for the associated field theories.

Solutions extend to D2-branes and other configurations.

Abstract

We present and analyze solutions of D=11 supergravity describing the ``near-horizon'' (i.e., asymptotically AdS_4 x S^7) geometry of M2-branes wrapped on surfaces of arbitrary genus. We study the forces experienced by test M2-branes in such backgrounds, and find evidence that extremal branes on surfaces of genera higher than the torus are unstable. Using the holographic connection between AdS spaces and superconformal field theories in the large N limit, we discuss the phases of the associated 2+1 dimensional theories. Finally, we also study the extension of these solutions to other branes, in particular to D2-branes.