Two-dimensional (0,2) theories and resolved An singularities

In this paper, we study (0,2) two-dimensional theories in type IIB configurations with D5 branes wrapping blow-up [Formula: see text] cycles of deformed resolutions for [Formula: see text] singularities or in T-dual IIA configurations with suspended D4 branes. We consider deformations of four-dimensional [Formula: see text], [Formula: see text] theories with general superpotentials for the adjoint and bifundamental fields together with fundamental flavors and reduce to two dimensions on a two-torus in the presence of magnetic fluxes and FI terms.