Geometric Constructions of Two Dimensional (0,2) SUSY Theories

TL;DR

This paper explores geometric methods to construct two-dimensional (0,2) supersymmetric theories using D5 branes wrapped on cycles in conifold geometries, analyzing supersymmetry preservation, flux relations, and geometric transitions.

Contribution

It introduces a geometric framework for (0,2) SUSY theories via D5 branes on conifold cycles, linking fluxes, moduli, and supersymmetry conditions, and relates to prior brane configurations.

Findings

Preservation of (0,2) supersymmetry under specific flux-moduli relations

Geometric interpretation of D-term and magnetic flux equality

Partial supersymmetry breaking after geometric transitions

Abstract

We consider the field theories on multiple stacks of D5 branes wrapped on four cycles of resolved/deformed conifold geometries fibered over a two torus. The central charges of the D5 branes are slightly misaligned when the branes are wrapped on various rigid holomorphic two cycles or when they have different charges with respect to a magnetic flux turned on the two torus. The wrapped D5 branes preserve (0,2) supersymmetry in two dimensions if the Kahler moduli and the magnetic flux are related. Our geometries are T-dual to the brane configurations considered by Kutasov-Lin and we provide a geometric interpretation for their equality between the field theory D-terms and the magnetic fluxes. We also consider the geometric transitions for rigid holomorphic two cycles fibered over a two torus with magnetic flux and discuss the partial breaking of supersymmetry after the geometric transitions.