A McKay-like correspondence for $(0, 2)$-deformations

Abstract

We present a local computation of deformations of the tangent bundle for a resolved orbifold singularity C d =G. These correspond to (0; 2)-deformations of (2; 2)-theories. A McKay-like correspondence is found predicting the dimension of the space of rst-order deformations from simple calculations involving the group. This is conrmed in two dimensions using the Kronheimer{Nakajima quiver construction. In higher dimensions such a computation is subject to nontrivial worldsheet instanton corrections and some examples are given where this happens. However, we conjecture that the special crepant resolution given by the GHilbert scheme is never subject to such corrections, and show this is true in an innite number of cases. Amusingly, for three-dimensional examples where G is abelian, the moduli space is associated to a quiver given by the toric fan of the blow-up. It is shown that an orbifold of the form C 3 =Z7 has a nontrivial superpotential and thus an obstructed moduli space.