AdS Membranes Wrapped on Surfaces of Arbitrary Genus

TL;DR

This work constructs exact $D=11$ supergravity solutions describing the near-horizon region of M2-branes wrapped on genus-$g$ surfaces, yielding asymptotically $AdS_4\times S^7$ and enabling a holographic study of the dual $2+1$ SCFT at large $N$. By analyzing brane probes, it finds that extremal branes with genus $g>1$ are unstable due to repulsive forces, while spherical and toroidal cases behave differently, with toroidal branes marginally stable. The thermodynamic analysis maps to topological black-hole physics in $AdS_4$, showing no finite-volume phase transitions for $g>1$ and a ground state with nonzero entropy, though the appropriate reference state is subtle and probe results imply instability. The paper also discusses extending the construction to D2-branes, revealing a conformal-frame $AdS_4$ structure but encountering dilaton/time-dependence issues, and it outlines limitations regarding energy definitions and supersymmetry for non-toroidal topologies. Overall, the results illuminate how worldvolume topology influences stability and holographic phases, offering a framework for studying nontrivial M- and D-brane dynamics on curved horizons.

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.