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

TL;DR

The paper computes the conformal anomaly of the free six-dimensional ${\cal N}=(2,0)$ tensor multiplet on generic curved backgrounds using Seeley-DeWitt heat kernel methods. The anomaly is shown to decompose into a type A piece proportional to $E_6$ and a type B piece spanned by the Weyl invariants $I_1$, $I_2$, $I_3$, with the type B part reproducing the large-N M5-brane prediction up to an overall $4N^3$ factor, while the type A coefficient is different. The authors compute explicit coefficients for the scalar, fermion, and 2-form fields, assemble the tensor multiplet anomaly, and relate the results to the 2-, 3-, and 4-point stress-tensor correlators and to nonlocal terms in the effective action. They conclude that the type B sector captures the same $4N^3$ scaling as the interacting theory, illustrating how anomaly structures reflect AdS/CFT predictions and stress-tensor correlator data in six dimensions.

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.