BPS M5-branes as Defects for the 3d-3d Correspondence

TL;DR

This paper investigates supersymmetric M5-brane probes in an AdS_4 background from wrapped M5-branes, revealing how they create defects in the 3d-3d correspondence and relate to geometric structures like geodesics and Dehn surgery.

Contribution

It characterizes BPS M5-brane configurations as defects in the 3d-3d correspondence, linking geometric surfaces to supersymmetric probe branes and their symmetries.

Findings

BPS M5-branes wrap surfaces that are geodesics or tubular around geodesics in M_3.

Configurations preserve an extra U(1) symmetry beyond R-symmetry.

M2-branes stretch between M5-branes, relating to conformal Dehn surgery.

Abstract

We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surface embedded in an S^2-fibration over M_3. We find that the projection of this surface to M_3 can be either a geodesic or a tubular surface around a geodesic. These configurations preserve an extra U(1) symmetry, in addition to the one corresponding to the R-symmetry of the dual 3d N=2 gauge theory. BPS M2-branes can stretch between M5-branes wrapping geodesics. We interpret the addition of probe M5-branes on a closed geodesic in terms of conformal Dehn surgery.