Non-geometric fluxes and non-associative geometry

TL;DR

This paper explores non-commutative and non-associative structures in closed string theory, proposing a cyclic double commutator and tri-product to understand effects of geometric and non-geometric fluxes.

Contribution

It introduces a cyclic double commutator and a tri-product framework to analyze non-associative geometry in closed string backgrounds with fluxes.

Findings

Non-trivial cyclic double commutator indicates non-associativity.

Correlation functions suggest a tri-product capturing non-commutative effects.

Framework links flux backgrounds to non-associative geometry.

Abstract

In these proceedings, we discuss non-commutativity in closed string theory. In analogy to the open-string sector, for closed strings we first motivate a cyclic double commutator to be evaluated for backgrounds with geometric or non-geometric fluxes. A non-trivial result for such an expression indicates a non-associative structure. Second, we define a conformal field theory at linear order in background fluxes and compute correlation functions therein. From these we motivate a tri-product which captures non-commutative and non-associative effects.