Rational Curves and (0,2)-Deformations

Understand

We compare the count of (0,2)-deformation moduli fields for N=(2,2) conformal field theories on orbifolds and sigma-models on resolutions of the orbifold.

• The latter involves counting deformations of the tangent sheaf.
• We see there is generally a discrepancy which is expected to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution.
• We analyze the rational curves on the resolution to determine such corrections and discover that irreducible toric rational curves account for some, but not all, of the discrepancy.