Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7 \xd7 S4

Xinan Zhou,Simone Giombi,Nadav Drukker,Arkady A. Tseytlin

doi:10.1007/jhep07(2020)101

Abstract

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.

Highlights

Functions of operators inserted along it is controlled by the fluctuations [3] of the fundamental superstring near the static configuration
We use the holographic description to extract the defect CFT data associated to the surface operator
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

Summary

One-loop partition function: defect conformal anomaly

We calculate the fluctuation determinants about the AdS3 classical M2-brane solution. Here b2 tot = −6 = R(3) and as in string case, is proportional to the Euler number (assuming boundary terms are taken into account, cf footnote 30 in [3]) In any case, such divergences are absent in an analytic regularization like ζ-function one and may be ignored. It is remarkable that the structure of the partition function in the string and M2 cases is very similar This has to do, in particular, with the universal form of the Nambu-type term in the p-brane action and the fact that in a natural κ-symmetry gauge the fermionic kinetic term comes from the supergravity covariant derivative projected to the world volume that contains the F -flux term that gets contribution from the sphere magnetic part that is not sensitive to the details of surface in the AdS space.

Interpretation of the result

Non-supersymmetric surface defect and 2d RG flow

Defect 4-point correlation functions at large N from M2-brane action

The xxxx and xxyy correlators and Mellin representation

OPE analysis

Superconformal symmetry of holographic correlators

Twisted operators and supersymmetry

Fixing the yyyy correlator from the superconformal Ward identities

A D -functions