T-Duality, Jacobi Forms and Witten Gerbe Modules

TL;DR

This paper extends T-duality maps to graded versions, establishing isomorphisms of twisted cohomologies that preserve Jacobi form structures and constructing Witten gerbe modules with Jacobi form properties.

Contribution

It introduces graded Hori maps for T-duality, demonstrating their isomorphism of twisted cohomologies and linking gerbe modules to Jacobi forms.

Findings

Graded Hori maps induce isomorphisms of twisted cohomologies.

Witten gerbe modules have graded twisted Chern characters as Jacobi forms.

Composition of Hori map with its dual equals the Euler operator.

Abstract

In this paper, we extend the T-duality Hori maps in [arXiv:hep-th/0306062], inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of two-variable series of twisted cohomologies on the T-dual circle bundles, preserving Jacobi form properties. The composition of the graded Hori map with its dual equals the Euler operator. We also construct Witten gerbe modules arising from gerbe modules and show that their graded twisted Chern characters are Jacobi forms under an anomaly vanishing condition on gerbe modules, thereby giving interesting examples.