Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry

TL;DR

This paper explores how non-geometric string backgrounds lead to non-commutative and non-associative geometries, modeled by twisted Poisson structures, with implications for string theory and dualities.

Contribution

It introduces a mathematical framework using twisted Poisson structures to describe non-commutative and non-associative geometries in string theory.

Findings

Non-commutative and non-associative algebras arise in string backgrounds.

Twisted Poisson structures effectively model these geometries.

Analogies with magnetic monopoles clarify the mathematical structure.

Abstract

In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding effective action for these kind of non-geometric string backgrounds. As we will argue, the emerging non-commutative and non-associative algebras for the closed string (dual) coordinates and (dual) momenta can be mathematically described by a twisted Poisson structure, in closed analogy to the phase space of a point particle moving in the field of a magnetic monopole.