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 M3 or N3/2, the number of degrees of freedom of the M5- or M2-brane theory at large M or N , respectively.
Highlights
We present holographic calculations of this central charge for several maximally supersymmetric conformal field theory (CFT) 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
The 11d SUGRA soliton solution for M5-branes indicates that the worldvolume theory has 6d N = (2, 0) SUSY and that the worldvolume fields should consist of five scalars, a chiral two-form A2, and their fermionic superpartners filling out a tensor multiplet [13]
We find that none of the calculations of the central charge of the self-dual string or Wilson surface—b6d and b3d, Berman and Harvey (BH), Niarchos and Siampos (NS), and free ABJM — agree perfectly with any of the others, though some share certain features
Summary
The solutions of 11d SUGRA in ref. [26] that holographically describe Wilson surfaces or cousins of the ABJM BCFT (and which built upon the solutions in refs. [23,24,25]) are 1/2BPS, meaning they support 16 real supercharges, and have super-isometry D(2, 1; γ) × D(2, 1; γ) with γ ∈ R. The 11d SUGRA solutions holographically describing Wilson surfaces in the M5-brane theory at large M are of the form in eq (2.1) with h = −i (w − w) , G. where the integer n ≥ 0 and the ξj are 2n + 2 real-valued constants determining G’s branch points on the boundary of the upper half plane. The background geometry for the holographically dual field theory has coordinates t ∈ (−∞, ∞), x ∈ (−∞, ∞), and x⊥ ∈ [0, ∞), i.e. half of 3d Minkowski space with a boundary at x⊥ = 0 In this sense, these solutions are locally asymptotic to “half” of AdS4 × S7, as advertised. If we fix r and send u → 0, z → 0 but x⊥ → 0, and so we arrive at the AdS4 boundary precisely on the BCFT’s 2d boundary
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