# Courant bracket found out to be T-dual to Roytenberg bracket

## TL;DR

This paper demonstrates that the Courant bracket in bosonic string theory is T-dual to the Roytenberg bracket, revealing a deep connection between these mathematical structures in string backgrounds with fluxes.

## Contribution

It establishes the T-duality relationship between the Courant and Roytenberg brackets in string theory with fluxes, expanding understanding of dualities in generalized geometry.

## Key findings

- Courant bracket arises from generalized currents Poisson brackets in string theory.
- T-dual theory's Poisson brackets lead to the Roytenberg bracket.
- Courant and Roytenberg brackets are related via T-duality in flux backgrounds.

## Abstract

Bosonic string moving in coordinate dependent background fields is considered. We calculate the generalized currents Poisson bracket algebra and find that it gives rise to the Courant bracket. Furthermore, we consider the T-dual theory and obtain the dual generalized currents Poisson bracket algebra. It gives rise to the Roytenberg bracket. We conclude that the Courant bracket twisted with the Kalb-Ramond field is T-dual to the Roytenberg bracket, with $Q$ and $R$ flux.