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A new approach to topological T-duality for principal torus bundles

Tom Dove, Thomas Schick

Abstract

We introduce a new `Thom class' formulation of topological T-duality for principal torus bundles. This definition is equivalent to the established one of Bunke, Rumpf, and Schick but has the virtue of removing the global assumptions on the H-flux required in the old definition. With the new definition, we provide easier and more transparent proofs of the classification of T-duals and generalise the local formulation of T-duality for circle bundles by Bunke, Schick, and Spitzweck to the torus case.

A new approach to topological T-duality for principal torus bundles

Abstract

We introduce a new `Thom class' formulation of topological T-duality for principal torus bundles. This definition is equivalent to the established one of Bunke, Rumpf, and Schick but has the virtue of removing the global assumptions on the H-flux required in the old definition. With the new definition, we provide easier and more transparent proofs of the classification of T-duals and generalise the local formulation of T-duality for circle bundles by Bunke, Schick, and Spitzweck to the torus case.

Paper Structure

This paper contains 8 sections, 28 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. A Thom class formulation of T-Duality
  3. Existence of T-duals
  4. Global condition on the H-flux
  5. Uniqueness of T-duals
  6. Proof of Theorem \ref{['thm:pullbackThomclass']}
  7. A local definition of T-duality
  8. The T-duality transformation

Key Result

Theorem 1

A pair $(E, G)$ over a CW-complex $X$ has a T-dual if and only if $[G] \in \mathcal{F}^2 H^3(E)$.

Theorems & Definitions (63)

  • Definition 1.1
  • Theorem : Theorem \ref{['thm:existence']}
  • Theorem : Theorem \ref{['thm:uniqueness1']}
  • Proposition 2.1
  • proof
  • Definition 2.2
  • Definition 2.3
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • ...and 53 more