Wilson surface central charge from holographic entanglement entropy

Abstract

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.

Central charges of 2d superconformal defects

“…In fact, we will obtain a more general result: we will compute the shift in E c due to two intersecting Wilson surfaces, which turns out to be more than just a sum of the contributions from two individual Wilson surfaces, possibly because of additional degrees of freedom arising at the 1d intersections along S 1 R . Holographic results for b and d 2 exist for the 2d N = (4, 4) superconformal defects in N = 4 SYM theory, in the 't Hooft large-N limit with large 't Hooft coupling [21,26,36,88], and for Wilson surfaces in the M5-brane SCFT, in the large-N limit [21,25,26,35]. Our results using SUSY methods agree perfectly with the holographic results, whenever they overlap.…”

“…[32]. In general, b, d 1 , and d 2 are difficult to calculate, and indeed to our knowledge they have been calculated only in free-field CFTs [22,23,33,34] and holographic CFTs [21,25,26,[35][36][37][38][39][40][41][42][43][44][45]. This is why we turn to SUSY, to provide tractable examples of interacting theories in which we can calculate b, d 1 , and d 2 without using holography.…”

Holographic entanglement entropy from probe M-theory branes

“…We have computed the contribution to entanglement entropy from a number of defects in N = (2, 0) SCFT, holographically dual to probe M-theory branes, for a spherical entangling region centred on the defect. Some of these defects were Wilson surfaces, and for these the entanglement entropy reproduces the probe limit of the results of [20]. The contribution of a two-dimensional conformal defect to the entanglement entropy of a spherical subregion takes the same form as the entanglement entropy of a single interval in a two-dimensional CFT, and in particular is logarithmically divergent in the UV.…”

“…A subset of the defects we study are expected to be one-half BPS Wilson surface operators [16][17][18], and in these cases our results reproduce the probe limit of the calculations in refs. [19,20]. We will also study solutions dual to defect renormalization group (RG) flows between these Wilson surfaces and conformal defects dual to bundles of M2-branes.…”

Superconformal surfaces in four dimensions

“…After the initial study of [65,73], various other holographic computations were performed, both in four and six dimensions [28,29,31,32,[74][75][76][77][78][79][80]. To the best of our knowledge, however, all these results can be related to the value of b, i.e.…”