Aspects of the (0,2)-McKay Correspondence

<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form \CC³/\ZZ_r, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p>

Author dc:creator

• Gaines, Benjamin C.

Advisor dc:contributor.advisor

• Aspinwall, Paul S

• Mathematics
• Theoretical mathematics
• Theoretical physics
• Deformations
• Hilbert Scheme
• McKay
• Toric

Handle dc:identifier.uri

https://hdl.handle.net/10161/9863

OAI identifier oai:identifier

oai:dukespace.lib.duke.edu:10161/9863