Matrix theory origins of non-geometric fluxes

TL;DR

This paper investigates the origins of non-geometric fluxes in M theory using matrix models, revealing their relation to non-commutative and non-associative structures, and exploring dualities and gauge theories arising from these compactifications.

Contribution

It introduces a framework connecting non-geometric fluxes to deformations of tori with non-commutative and non-associative phase space structures within matrix theory.

Findings

Flux quantization emerges naturally from the framework.

Duality exchanges properties of geometric and non-geometric fluxes.

Insights into effective gauge theories from matrix compactifications.

Abstract

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and non-associative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of non-associativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.