Anomaly of (2,0) Theories

TL;DR

This work computes gravitational and axial anomalies for D-type $(2,0)$ theories realized on $N$ pairs of coincident M5-branes at the $R^5/Z_2$ orbifold fixed point. By extending the FHMM/HMM anomaly inflow framework to orbifold backgrounds and incorporating fixed-point contributions via consistency of $T^5/Z_2$, the authors derive the world-volume anomaly polynomial as $N{\cal J}_8 + N(2N-1)(2N-2)\frac{p_2({\cal N})}{24}$, in agreement with Intriligator's ADE conjecture. An independent untwisted-sector one-loop check supports the result modulo a local counter-term, strengthening the ADE-structured understanding of $(2,0)$ anomalies and pointing to further checks in AdS/CFT and extensions to E-type theories.

Abstract

We compute gravitational and axial anomaly for D-type (2,0) theories realized on N pairs of coincident M5-branes at R^5/Z_2 orbifold fixed point. We first summarize work by Harvey, Minasian, and Moore on A-type (2,0) theories, and then extend it to include the effect of orbifold fixed point. The net anomaly inflow follows when we further take into account the consistency of T^5/Z_2 M-theory orbifold. We deduce that the world-volume anomaly is given by N{\cal J}_8 + N(2N-1)(2N-2) p_2/24 where {\cal J}_8 is the anomaly polynomial of a free tensor multiplet and p_2 is the second Pontryagin class associated with the normal bundle. This result is in accord with Intriligator's conjecture.