Categorical symmetries of T-duality

TL;DR

This paper investigates the higher-categorical symmetries of topological T-duality by computing the automorphism group of the associated Lie 2-group, revealing its structure as a non-central extension with specific torsion properties.

Contribution

It explicitly computes the categorical automorphism group of the Lie 2-group classifying topological T-duality correspondences, uncovering its extension and torsion characteristics.

Findings

The automorphism group is a non-central extension of the integral split pseudo-orthogonal group.

It splits over several subgroups.

Its k-invariant is 2-torsion.

Abstract

Topological T-duality correspondences are higher categorical objects that can be classified by a strict Lie 2-group. In this article we compute the categorical automorphism group of this 2-group; hence, the higher-categorical symmetries of topological T-duality. We prove that the categorical automorphism group is a non-central categorical extension of the integral split pseudo-orthogonal group. We show that it splits over several subgroups, and that its k-invariant is 2-torsion.