Equivariant Topological T-Duality

Fuente: arXiv
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Main Authors: Dove, Tom, Schick, Thomas
Format: Preprint
Published: 2023
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author Dove, Tom
Schick, Thomas
author_facet Dove, Tom
Schick, Thomas
contents Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of the T-duality transformation: a T-duality relation between pairs (E, P ) and (F, Q ) comes with an isomorphism (with degree shift) between the twisted K-theory of E and the twisted K-theory of F. We formulate topological T-duality in the equivariant setting, following the definition of Bunke, Rumpf, and Schick. We define the T-duality transformation in equivariant K-theory and show that it is an isomorphism for actions of compact Lie groups, equal to its own inverse and uniquely characterized by naturality and a normalization for trivial situations.
format Preprint
id arxiv_https___arxiv_org_abs_2310_06064
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Equivariant Topological T-Duality
Dove, Tom
Schick, Thomas
K-Theory and Homology
High Energy Physics - Theory
Mathematical Physics
Geometric Topology
Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of the T-duality transformation: a T-duality relation between pairs (E, P ) and (F, Q ) comes with an isomorphism (with degree shift) between the twisted K-theory of E and the twisted K-theory of F. We formulate topological T-duality in the equivariant setting, following the definition of Bunke, Rumpf, and Schick. We define the T-duality transformation in equivariant K-theory and show that it is an isomorphism for actions of compact Lie groups, equal to its own inverse and uniquely characterized by naturality and a normalization for trivial situations.
title Equivariant Topological T-Duality
topic K-Theory and Homology
High Energy Physics - Theory
Mathematical Physics
Geometric Topology
url https://arxiv.org/abs/2310.06064