Holographic M5 branes in $AdS_7\times S^4$

TL;DR

This paper investigates classical M5 brane solutions in AdS_7 x S^4, revealing their holographic duals as codimension-2 defects in 6d supersymmetric theories, characterized by holomorphic functions and boundary behaviors.

Contribution

It provides a new class of BPS M5 brane solutions described by holomorphic functions, advancing understanding of holographic duals of defects in 6d theories.

Findings

Solutions described by holomorphic functions satisfying a scaling condition

Characterization of boundary behavior via intersections of zeros of holomorphic functions

Insights into the geometry of M5 branes near the AdS boundary

Abstract

We study classical M5 brane solutions in the probe limit in the $AdS_7\times S^4$ background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual N=(0,2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.