Wilson surface central charge from holographic entanglement entropy

A bstract We use entanglement entropy to define a central charge associated to a twodimensional 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 N M2-branes ending on M M5-branes. 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.