Abelian M5-brane on S6

Abstract

We study the abelian M5 brane on S6. From the spectrum we extract a series expansion for the heat kernel. In particular we determine the normalization for the coefficient a in the M5 brane conformal anomaly. When we compare our result with what one gets by computing the Hadamard-Minakshisundaram-DeWitt-Seeley coefficients from local curvature invariants on S6, we first find a mismatch of one unit. This mismatch is due to an overcounting of one zero mode. After subtracting this contribution, we finally find agreement. We perform dimensional reduction along a singular circle fiber to five dimensions where we find the conformal anomaly vanishes.