Anomaly Cancellation and Modularity

TL;DR

This paper demonstrates that key anomaly cancellation formulas in string theory can be derived from the modularity of characteristic forms, unifying several formulas within a single mathematical framework.

Contribution

It unifies the derivation of multiple anomaly cancellation formulas in string theory using modularity of characteristic forms, extending their generalizations.

Findings

Unified derivation of anomaly cancellation formulas

Extension of formulas to broader contexts

New generalizations of known anomaly cancellation formulas

Abstract

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula in type I superstring theory can also be derived from the modularity of those characteristic forms and thus unify the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten formula, the Green-Schwarz formula as well as the Schwarz-Witten formula in the same framework. Various generalizations of these remarkable formulas are also established.