2d (0,2) Quiver Gauge Theories and D-Branes

TL;DR

This paper develops methods to systematically construct and analyze 2d (0,2) quiver gauge theories arising from D1-branes probing toric Calabi-Yau 4-folds, introducing new computational tools and brane configurations.

Contribution

It introduces an algorithm for calculating moduli spaces, a systematic construction procedure via partial resolution, and the novel Brane Brick Models linking geometry and gauge theories.

Findings

Efficient calculation of classical mesonic moduli spaces.

Systematic construction of gauge theories for arbitrary toric singularities.

Introduction of Brane Brick Models as a 2d analogue of Brane Tilings.

Abstract

We initiate a systematic study of 2d (0,2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are the 2d analogues of Brane Tilings and allow a direct connection between geometry and gauge theory.