TY - JOUR

T1 - Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7 × S 4

AU - Drukker, Nadav

AU - Giombi, Simone

AU - Tseytlin, Arkady A.

AU - Zhou, Xinan

N1 - Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Publisher Copyright:
© 2020, The Author(s).

PY - 2020/7/1

Y1 - 2020/7/1

N2 - Surface operators in the 6d (2,0) theory at large N have a holographic description in terms of M2 branes probing the AdS7×S4 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 d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS3 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 N0. 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 AdS3 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 sub- sector of “twisted” scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.

AB - Surface operators in the 6d (2,0) theory at large N have a holographic description in terms of M2 branes probing the AdS7×S4 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 d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS3 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 N0. 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 AdS3 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 sub- sector of “twisted” scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.

KW - AdS-CFT Correspondence

KW - Anomalies in Field and String Theories

KW - Conformal Field Theory

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U2 - 10.1007/JHEP07(2020)101

DO - 10.1007/JHEP07(2020)101

M3 - Article

AN - SCOPUS:85088110356

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 101

ER -