SL(2,Z) Modular Forms and Anomaly Cancellation Formulas II

TL;DR

This paper constructs new modular forms related to SL(2,Z) and derives anomaly cancellation formulas for spin and spin^c manifolds, leading to divisibility results for Dirac operator indices.

Contribution

It introduces novel modular forms and applies them to establish new anomaly cancellation formulas and divisibility properties for manifold indices.

Findings

New modular forms for a0(a0) and a0(a0) constructed.

Derived new anomaly cancellation formulas for spin and spin^c manifolds.

Established divisibility results for indices of twisted Dirac operators.

Abstract

By some SL(2, Z) modular forms introduced in [4] and [9], we construct some {\Gamma}^0(2) and {\Gamma}_0(2) modular forms and obtain some new cancellation formulas for spin manifolds and spin^c manifolds respectively. As corollaries, we get some divisibility results of index of twisted Dirac operators on spin manifolds and spin^c manifolds .