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

Abstract

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.

Surface operators in superspace

“…Surface operators exhibit a conformal anomaly [27], as expected for all even dimensional defects. The anomaly in six dimensions has been determined perturbatively [17,19,28,29] and holographically [24,30], and the results are consistent with what has been obtained from the entanglement entropy for the bubbling M5/M2 geometry [31,32], and exactly from the determination of the corresponding superconformal index [33].…”

“…and coincides with the operator introduced in [17] and more recently studied in [18,19,24], which includes couplings to the five scalar fields ϕ [AB] of the tensor multiplet, in analogy with the Wilson-Maldacena loop.…”

“…Correlation functions of WS's, and WS with local operators, Wilson and 't Hooft loops in four [20][21][22] and six [23,24] dimensions have been computed, perturbatively or using (super)conformal techniques or the dual supergravity description. The dual description has also been used to compute the Operator Product Expansion of surface operators in the large N limit [23,25,26].…”

Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1

“…Topological sectors, hopefully amenable to localization, could appear considering other supermultiplets [34]: if this is the case, the study of more general correlators might be interesting. It would be also interesting to extend these investigations to non-supersymmetric lines in ABJM, as done in [48] for N = 4 SYM, or to higher-dimensional defects [49].…”

“…19 By evaluating perturbatively the two-point function (5.17) (namely, calcu- 18 This is the formal choice of [5], where the analogue relation is to the N = 4 SYM Bremsstrahlung function [10,82,83]. See also a related discussion in [49]. 19 Given the leading strong coupling value of the Bremsstrahlung function B 1/2 (λ) = √ 2λ 4π ≡ T 2π , and given our choice (5.19) of the bulk-to-boundary propagator, at tree level this would amount to the rescaling w a → √ 2T w a .…”