Brane Box Realization of Chiral Gauge Theories in Two Dimensions

TL;DR

This paper explores how brane box configurations in type IIA string theory can realize two-dimensional chiral gauge theories with various supersymmetries, linking brane setups to singularity geometries and supersymmetry enhancements.

Contribution

It establishes a method to derive the spectrum and interactions of 2D gauge theories from brane configurations and connects these to D1 branes at singularities, elucidating supersymmetry enhancements.

Findings

Rules for reading off spectrum and interactions from brane configurations

Mapping brane setups to D1 branes at singularities

Geometric interpretation of supersymmetry enhancement

Abstract

We study type IIA configurations of D4 branes and three kinds of NS fivebranes. The D4 brane world-volume has finite extent in three directions, giving rise to a two-dimensional low-energy field theory. The models have generically $(0,2)$ supersymmetry. We determine the rules to read off the spectrum and interactions of the field theory from the brane box configuration data. We discuss the construction of theories with enhanced $(0,4)$, $(0,6)$ and $(0,8)$ supersymmetry. Using T-duality along the directions in which the D4 branes are finite, the configuration can be mapped to D1 branes at $\IC^4/\Gamma$ singularities, with $\Gamma$ an abelian subgroup of SU(4). This provides a rederivation of the rules in the brane box model. The enhancement of supersymmetry has a nice geometrical interpretation in the singularity picture in terms of the holonomy group of the four-fold singularity.