T-Duality, Jacobi Forms and Witten Gerbe Modules

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.

arXiv comment24 pages, minor corrections, references added

References in corpus (8)

• Twisted K-theory and K-theory of bundle gerbes
• Algebraic topology and modular forms
• On the Topology and Flux of T-Dual Manifolds
• Modular Invariance and Characteristic Numbers
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Cited by in corpus (3)

• T-duality with $H$-flux for $2d$ $\sigma$-models
• T-duality, vertical holonomy line bundles and loop Hori formulae
• A very short note on the (rational) graded Hori map