# Wilson Surface Central Charge from Holographic Entanglement Entropy

## TL;DR

This paper defines a holographic central charge for defects in conformal field theories using entanglement entropy, calculating it for various M-brane configurations and analyzing its scaling behavior.

## Contribution

It introduces a new holographic central charge for 2D defects in CFTs and provides explicit calculations for M-brane theories with detailed dependence on brane partitions.

## Key findings

- Central charge depends on M2- and M5-brane partitions.
- Results expressed in terms of algebraic data like Weyl vectors.
- Central charge scaling differs from naive degrees of freedom expectations.

## Abstract

We use entanglement entropy to define a central charge associated to a two-dimensional defect or boundary in a conformal field theory (CFT). We present holographic calculations of this central charge for several maximally supersymmetric CFTs dual to eleven-dimensional supergravity in Anti-de Sitter space, namely the M5-brane theory with a Wilson surface defect and three-dimensional CFTs related to the M2-brane theory with a boundary. Our results for the central charge depend on a partition of the number of M2-branes, $N$, ending on the number of M5-branes, $M$. For the Wilson surface, the partition specifies a representation of the gauge algebra, and we write our result for the central charge in a compact form in terms of the algebra's Weyl vector and the representation's highest weight vector. We explore how the central charge scales with $N$ and $M$ for some examples of partitions. In general the central charge does not scale as $M^3$ or $N^{3/2}$, the number of degrees of freedom of the M5- or M2-brane theory at large $M$ or $N$, respectively.