Twisted C-brackets

TL;DR

This paper explores the algebra of symmetry generators in double field theory for closed bosonic strings, deriving twisted C-brackets influenced by background fields and T-duality, revealing their mathematical structure and relations.

Contribution

It introduces twisted C-brackets in double field theory, incorporating effects of the Kalb-Ramond field and non-commutativity, expanding understanding of symmetry algebra in string theory.

Findings

Derived B-twisted C-bracket with Kalb-Ramond field

Derived θ-twisted C-bracket with non-commutativity parameter

Commented on relations to twisted Courant brackets and T-duality

Abstract

We consider the double field formulation of the closed bosonic string theory, and calculate the Poisson bracket algebra of the symmetry generators governing both general coordinate and local gauge transformations. Parameters of both of these symmetries depend on a double coordinate, defined as a direct sum of the initial and T-dual coordinate. When no antisymmetric field is present, the $C$-bracket appears as the Lie bracket generalization in a double theory. With the introduction of the Kalb-Ramond field, the $B$-twisted $C$-bracket appears, while with the introduction of the non-commutativity parameter, the $\theta$-twisted $C$-bracket appears. We present the derivation of these brackets and comment on their relations to analogous twisted Courant brackets and T-duality.