Holographic entanglement entropy from probe M-theory branes

Surface operators in the 6d (2,0) theory at large N have a holographic description in terms of M2 branes probing the AdS 7 × S 4 M-theory background. The most symmetric, 1/2-BPS, operator is defined over a planar or spherical surface, and it preserves a 2d superconformal group. This includes, in particular, an SO(2, 2) subgroup of 2d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS 3 induced geometry, reflecting the 2d conformal symmetry. Here we use the holographic description to extract the defect CFT data associated to the surface operator. The spectrum of transverse fluctuations of the M2 brane is found to be in one-to-one correspondence with a protected multiplet of operator insertions on the surface, which includes the displacement operator. We compute the one-loop determinants of fluctuations of the M2 brane, and extract the conformal anomaly coefficient of the spherical surface to order N 0. We also briefly discuss the RG flow from the non-supersymmetric to the 1/2-BPS defect operator, and its consistency with a "b-theorem" for the defect CFT. Starting with the M2 brane action, we then use AdS 3 Witten diagrams to compute the 4-point functions of the elementary bosonic insertions on the surface operator, and extract some of the defect CFT data from the OPE. The 4-point function is shown to satisfy superconformal Ward identities, and we discuss a related subsector of "twisted" scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.

Section: Jhep07(2020)101mentioning

confidence: 83%

Section: Ope Analysismentioning

confidence: 99%

See 1 more Smart Citation

Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7 × S4

Drukker

Giombi

Tseytlin

et al. 2020

“…[26,102] showed that for a 2d conformal defect in a higher-d CFT, the entanglement entropy of a sphere centred on the defect includes a logarithmic term with a universal coefficient given by a linear combination of three central charges: the ambient CFT's type A central charge (when d is even), b, and d 2 . [25,26,103,104]. One of our goals is to reproduce these results using purely field theory means, so let us review them in detail.…”

Section: Holographic Resultsmentioning

confidence: 99%

“…A Wilson surface defect is labelled by a Young tableau corresponding to a representation of su(N ) with highest weight ω. The holographic results for b and d 2 for a Wilson surface are[25,26,103,104]…”

mentioning

confidence: 99%

Central charges of 2d superconformal defects

Chalabi

O’Bannon

Robinson

et al. 2020

In conformal field theories (CFTs) of dimension d > 3, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect's contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on S d with defect along S 2 , or on S 1 × S d−1 with defect along S 1 × S 1. In the latter case we propose that defect central charges appear in an overall normalisation factor, as part of the SUSY Casimir energy. For 2d half-BPS defects in 4d N = 2 SCFTs and in the 6d N = (2, 0) SCFT we obtain novel, exact results for defect central charges using existing results for partition functions computed using SUSY localisation, SUSY indices, and correspondences to 2d Liouville, Toda, and q-deformed Yang-Mills theories. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large-N and/or strongcoupling limits, but are exact. Our methods can be straightforwardly extended to other superconformal defects, of various codimension, as we demonstrate for a 4d defect in the 6d N = (2, 0) SCFT.

M2-doughnuts

Drukker

Trépanier

2022

We present a family of new M2-brane solutions in AdS7× S4 that calculate toroidal BPS surface operators in the $$ \mathcal{N} $$ N = (2, 0) theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large N. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail.