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

Abstract

We compute the conformal anomaly in the free d = 6 superconformal (2,0) tensor multiplet theory on generic curved background. Up to a trivial covariant totalderivative 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 conformal invariants: two CCC contractions of Weyl tensors and a C?2C + ... term. Multiplied by the factor 4N3, the latter Weyl-invariant 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 AdS7 supergravity on the basis of AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor 4 7 ? 4N3, so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient 4N3 is the same as found (hep-th/9703040) in the comparison of the tensor multiplet theory and the d = 11 supergravity predictions for the absorption crosssections 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 AdS7 supergravity predictions. The reason for this coincidence is that the three Weyl-invariant terms in the anomaly are related to the h2 and h3 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 h4 term in the non-local part of the effective action, i.e. to a certain structure in the 4-point correlation function of the stress tensors. It should thus capture some non-trivial dynamics of the interacting theory. This is different from what happens in the d = 4 SYM case where the type B and type A anomalies are related to the 2-point and 3-point stress tensor correlators.