(0,2) Deformations of Linear Sigma Models

Understand

We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma model for a Calabi-Yau hypersurface in a Fano toric variety.

• In the non-linear sigma model these correspond to some of the holomorphic deformations of the tangent bundle on the hypersurface.
• Combinatorial formulas are given for the number of these deformations, and we show that these numbers are exchanged by mirror symmetry in a subclass of the models.