# Hidden isometry of "T-duality without isometry"

## TL;DR

This paper reveals that the so-called 'T-duality without isometry' is actually a form of traditional isometric non-Abelian T-duality, once the appropriate framing is chosen, clarifying the true nature of the duality.

## Contribution

The authors demonstrate that the T-dualisability criteria depend on the choice of framing and that the proposed 'without isometry' duality is equivalent to standard isometric T-duality.

## Key findings

- T-dualisability criteria are framing-dependent.
- Existence of an isometric framing simplifies the gauging process.
- 'T-duality without isometry' is equivalent to traditional isometric T-duality.

## Abstract

We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke [3] who recently used Lie algebroid gauge theories to obtain sigma models exhibiting a "T-duality without isometry". We point out that those T-dualisability criteria are not written invariantly in [3] and depend on the choice of the algebroid framing. We then show that there always exists an isometric framing for which the Lie algebroid gauging boils down to standard Yang-Mills gauging. The "T-duality without isometry" of Chatzistavrakidis, Deser and Jonke is therefore nothing but traditional isometric non-Abelian T-duality in disguise.