Flux corrections to anomaly cancellation in M-theory on a manifold with boundary

TL;DR

This paper investigates how flux couplings affect anomaly cancellation in M-theory on manifolds with boundaries, providing corrected formulas and discussing potential numerical inaccuracies in the Dirac operator coefficients.

Contribution

It introduces flux corrections to anomaly cancellation in M-theory with boundary manifolds and computes the first nontrivial correction, refining previous theoretical models.

Findings

Anomaly cancellation persists with flux couplings after gauge current shifts.

First nontrivial flux correction to anomaly cancellation is computed.

Authors caution about potential numerical inaccuracies in Dirac operator coefficients.

Abstract

We show how the coupling of gravitinos and gauginos to fluxes modifies anomaly cancellation in M-theory on a manifold with boundary. Anomaly cancellation continues to hold, after a shift of the definition of the gauge currents by a local gauge invariant expression in the curvatures and E8 fieldstrengths. We compute the first nontrivial correction of this kind. Warning: Ian Moss has called into question several of the numerical coefficients in the extended Dirac operators in this paper. We have not confirmed this but the reader is warned not to trust the precise coefficients in the formulae for the Dirac operators and heat kernel expansions. We believe these possible errors do not change our qualitative conclusions. One of us intends to return to the issue and recheck the formulae. We thank Ian Moss for pointing out these problems.