Brackets in bosonic string theory

TL;DR

This paper reviews brackets and interior products in bosonic string theory, focusing on the C-bracket in double string theory, its mathematical properties, and connections to Courant algebroids and Poisson algebra.

Contribution

It provides a comprehensive review of brackets in bosonic string theory, highlighting the C-bracket's relation to Poisson algebra and Courant algebroids, and explores their mathematical structures.

Findings

C-bracket's connection to Poisson algebra of symmetry generators

Relation of brackets to Courant algebroid structures

Analysis of anomaly reduction in bracket transformations

Abstract

We give a review of brackets and interior products in bosonic string theory, in different representations, used in formulation of a theory and derived in a transformation of related mathematical structures. We consider the C-bracket, defined in double string theory, in a context of Poisson algebra of symmetry generator, and show its connection to prior brackets trough anomaly reduction, and its characteristics related to Courant algebroid definitions.