Nonassociative Gravity in String Theory?

TL;DR

This paper explores the possibility of a nonassociative gravity theory emerging from string theory, based on a three-bracket structure in closed string backgrounds with flux, suggesting a new form of noncommutative geometry.

Contribution

It introduces the concept of a three-bracket structure in closed string backgrounds, extending noncommutative gauge theories to a nonassociative gravity framework.

Findings

Indications of a three-bracket structure in target space coordinates.

Proposal of a generalized uncertainty principle.

Discussion of implications for noncommutative/nonassociative gravity.

Abstract

In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative gauge theories for open strings in two-form backgrounds to a putative noncommutative/nonassociative gravity theory for closed strings probing curved backgrounds with non-vanishing three-form flux. Several aspects and consequences of the three-bracket structure are discussed and a new type of generalized uncertainty principle is proposed.