Chern-kernels and anomaly cancellation in M-theory

TL;DR

This paper introduces Chern-kernels as an alternative to Dirac-branes for solving magnetic equations in M-theory, leading to anomaly cancellation and consistent effective actions for branes.

Contribution

It proposes a new class of solutions using Chern-kernels, addressing singularities and anomaly issues in M-theory brane configurations.

Findings

Chern-kernels resolve singularities in magnetic field solutions.

Anomaly cancellation is achieved through the unobservability condition.

Provides an anomaly-free effective action for open M2-branes ending on M5-branes.

Abstract

This paper deals with magnetic equations of the type dH=J where the current J is a delta-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.