T-duality, Fiber Bundles and Matrices

TL;DR

This paper extends T-duality in gauge theory to curved spaces modeled as fiber bundles, offering new insights into truncation, vacua relations, and specific examples like S^3, S^5, and the Heisenberg nilmanifold.

Contribution

It introduces a framework for applying T-duality to gauge theories on curved fiber bundle spaces, including a novel perspective on truncation and vacua correspondence.

Findings

T-duality extended to curved fiber bundle spaces

New viewpoint on consistent truncation and vacua relations

Examples include S^3/Z_k, S^5/Z_k, and Heisenberg nilmanifold

Abstract

We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation between the vacua on the total space and on the base space. As examples, we consider S^3(/Z_k), S^5(/Z_k) and the Heisenberg nilmanifold.