Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence

TL;DR

This paper calculates the conformal anomaly of a six-dimensional (2,0) tensor multiplet, showing its relation to M5-brane theories and the AdS/CFT correspondence, with implications for stress tensor correlators.

Contribution

It provides the explicit form of the conformal anomaly for the free (2,0) tensor multiplet in six dimensions and connects it to large N M5-brane theories via AdS/CFT.

Findings

Type B anomaly matches the large N M5-brane prediction when scaled by 4N^3.

Type A anomaly differs by a factor of 4/7, indicating non-vanishing on Ricci-flat backgrounds.

Coefficients relate to stress tensor correlators and effective action expansions.

Abstract

We compute the conformal anomaly of free d=6 superconformal (2,0) tensor multiplet on generic curved background. Up to a trivial covariant total-derivative term, it is given by the sum of the type A part proportional to the 6-d Euler density, and the type B part containing three independent Weyl invariants. Multiplied by factor 4N^3, the type B part of the anomaly reproduces exactly the corresponding part of the conformal anomaly of large N multiple M5-brane (2,0) theory as predicted (hep-th/9806087) by the AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor 4/7 x 4 N^3, so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient 4N^3 is the same as found (hep-th/9703040) in the comparison of the tensor multiplet theory and the d=11 supergravity results for the absorption cross-sections of gravitons by M5 branes, and in the comparison (hep-th/9911135) of 2- and 3-point stress tensor correlators of the free tensor multiplet with the AdS_7 supergravity predictions. The reason for this coincidence is that the three Weyl-invariant terms in the anomaly are related to the $h^2$ and $h^3$ terms in the near flat space expansion of the corresponding non-local effective action, and thus to the 2-point and 3-point stress tensor correlators in flat background. At the same time, the type A anomaly is related to the $h^4$ term in the non-local part of the effective action, i.e. to a certain structure in the 4-point correlation function of stress tensors.