Deformations and D-branes

TL;DR

This paper explores the connection between Hochschild cohomology and physical states in topological string theory, linking deformations of derived categories to geometric and gauge theory deformations, including noncommutative aspects.

Contribution

It introduces an intrinsic notion of deformation within the derived category framework and maps noncommutative deformations to superpotential terms in D-brane gauge theories.

Findings

Hochschild cohomology relates to physical states in topological strings.

Deformations of quiver gauge theories correspond to geometric deformations of singularities.

Explicit mapping from noncommutative deformations to superpotential terms is provided.

Abstract

I discuss the relation of Hochschild cohomology to the physical states in the closed topological string. This allows a notion of deformation intrinsic to the derived category. I use this to identify deformations of a quiver gauge theory associated to a D-branes at a singularity with generalized deformations of the geometry of the resolution of the singularity. An explicit map is given from noncommutative deformations (ie, B-fields) to terms in the superpotential.