Anomalies of E8 gauge theory on String manifolds

TL;DR

This paper investigates anomaly cancellation in string and M-theory on String manifolds, revealing no E8 x E8 global anomaly, extending phase descriptions, and refining invariants using the Witten genus.

Contribution

It demonstrates the absence of E8 x E8 anomalies on String manifolds and extends key anomaly phase laws from Spin to String structures.

Findings

No E8 x E8 global anomaly on String manifolds

Extension of M-theory phase description from Spin to String case

Refinement of the one-loop term via the Witten genus

Abstract

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory partition function of Diaconescu-Moore-Witten extends from the Spin case to the String case. Third, that the cubic refinement law of Diaconescu-Freed-Moore for the phase of the M-theory partition function extends to String manifolds. The analysis relies on extending from invariants which depend on the Spin structure to invariants which instead depend on the String structure. Along the way, the one-loop term is refined via the Witten genus.