Several new $SL(2,Z)$ modular forms and anomaly cancellation formulas

TL;DR

This paper constructs new $SL(2,Z)$ modular forms on manifolds of various dimensions and derives novel anomaly cancellation formulas and applications, expanding previous work that focused on 12-dimensional cases.

Contribution

It introduces several new $SL(2,Z)$ modular forms applicable to manifolds of arbitrary dimension and establishes new anomaly cancellation formulas and related applications.

Findings

New $SL(2,Z)$ modular forms for various dimensions

Derived novel anomaly cancellation formulas

Extended previous 12-dimensional results to general dimensions

Abstract

In \cite{HLZ2} and \cite{HHLZ}, using $E_8$ bundles, some modular forms over $SL(2,{\bf Z})$ were constructed on $12$-dimensional manifolds and the Witten-Freed-Hopkins anomaly cancellation formula was derived by these $SL(2,Z)$ modular forms. In this paper, we construct several similar $SL(2,Z)$ modular forms on any dimensional manifolds and some new anomaly cancellation formulas and applications are given.