Chern–kernels and anomaly cancellation in M–theory

This paper deals with magnetic equations of the type dH = J where the current J is a δ–function on a brane worldvolume and H a p–form field strength. In many situations in M–theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac–branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern–kernels, and provide relevant applications, among which the anomaly–free effective action for open M2–branes ending on M5–branes. The unobservability of the Dirac–brane requires a Dirac quantization condition; we show that the requirement of “unobservability” of the Chern–kernel leads in M–theory to classical gravitational anomalies which cancel precisely their quantum counterparts. PACS: 11.15.-q, 11.10.Kk, 11.30.Cp;