Kavli Affiliate: Xinan Zhou
| First 5 Authors: Nadav Drukker, Simone Giombi, Arkady A. Tseytlin, Xinan Zhou,
| Summary:
Surface operators in the 6d (2,0) theory at large $N$ have a holographic
description in terms of M2 branes probing the AdS$_7 times S^4$ 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.
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