# From N=2 in four dimensions to (0,2) in two dimensions

## TL;DR

This paper explores how four-dimensional N=2 theories compactified on a torus with magnetic fields can lead to two-dimensional theories with different supersymmetry, focusing on geometric and brane configurations.

## Contribution

It analyzes the conditions under which compactified N=2 theories yield (2,2) or (0,2) supersymmetric theories in two dimensions, using brane and Calabi-Yau geometries.

## Key findings

- Conditions for (2,2) and (0,2) supersymmetry in 2D theories
- Relation between brane configurations and supersymmetry
- Impact of magnetic fields on compactification outcomes

## Abstract

We consider N=2 four dimensional field theories compactified on a two torus in the presence of a U(1) magnetic field. We discuss the restrictions leading to theories with (2,2) supersymmetry or (0,2) supersymmetry in two dimensions. The field theories live on D5 branes wrapped on four cycles of Calabi-Yau 3-folds or 4-folds described as resolved ADE singularities or resolved conifold fibered over a two torus.