Coisotropic Branes, Noncommutativity, and the Mirror Correspondence

TL;DR

This paper explores coisotropic A-branes in a four-torus sigma model, revealing their morphisms relate to noncommutative algebra and confirming mirror symmetry through morphism dimension comparisons.

Contribution

It explicitly constructs coisotropic branes, links their morphisms to noncommutative algebra, and verifies mirror symmetry in this context.

Findings

Morphisms between coisotropic branes correspond to noncommutative algebra representations.

Noncommutativity parameter relates to bundle data on branes.

Mirror symmetry is supported by matching morphism space dimensions.

Abstract

We study coisotropic A-branes in the sigma model on a four-torus by explicitly constructing examples. We find that morphisms between coisotropic branes can be equated with a fundamental representation of the noncommutatively deformed algebra of functions on the intersection. The noncommutativity parameter is expressed in terms of the bundles on the branes. We conjecture these findings hold in general. To check mirror symmetry, we verify that the dimensions of morphism spaces are equal to the corresponding dimensions of morphisms between mirror objects.