# Open-String Non-Associativity in an R-flux Background

## TL;DR

This paper demonstrates that open strings in R-flux backgrounds exhibit a non-associative algebraic structure, suggesting the emergence of non-associative gauge theories on D-branes in non-geometric spaces.

## Contribution

It derives the non-associative phase-space algebra for open strings in R-flux backgrounds, extending the understanding of non-geometric flux effects from closed to open strings.

## Key findings

- Open strings in R-flux backgrounds have non-associative algebraic structures.
- The effective gauge theory on D-branes in such backgrounds is expected to be non-associative.
- Differences between open and closed string non-associativity are linked to world-sheet commutator structures.

## Abstract

We derive the commutation relations for open-string coordinates on D-branes in non-geometric background spaces. Starting from D0-branes on a three-dimensional torus with H-flux, we show that open strings with end points on D3-branes in a three-dimensional R-flux background exhibit a non-associative phase-space algebra, which is similar to the non-associative R-flux algebra of closed strings. Therefore, the effective open-string gauge theory on the D3-branes is expected to be a non-associative gauge theory. We also point out differences between the non-associative phase space structure of open and closed strings in non-geometric backgrounds, which are related to the different structure of the world-sheet commutators of open and closed strings.