Undoing Orbifold Quivers

TL;DR

This paper explores the derivation of quiver gauge theories from D-branes at singularities, focusing on resolving orbifolds and proposing autoequivalences in derived categories, with implications for AdS/CFT correspondence.

Contribution

It introduces a method to obtain quivers by undoing orbifolds via McKay correspondence and conjectures an autoequivalence for orbifold group actions on derived categories.

Findings

Derived quivers for sphere and T^{11} obtained by undoing orbifolds.

Proposed autoequivalence implements orbifold group action on derived categories.

New autoequivalence identified for Z_2 quotient of the conifold.

Abstract

A number of new papers have greatly elucidated the derivation of quiver gauge theories from D-branes at a singularity. A complete story has now been developed for the total space of the canonical line bundle over a smooth Fano 2-fold. In the context of the AdS/CFT conjecture, this corresponds to eight of the ten regular Sasaki-Einstein 5-folds. Interestingly, the two remaining spaces are among the earliest examples, the sphere and T^{11}. I show how to obtain the (well-known) quivers for these theories by interpreting the canonical line bundle as the resolution of an orbifold using the McKay correspondence. I then obtain the correct quivers by undoing the orbifold. I also conjecture, in general, an autoequivalence that implements the orbifold group action on the derived cateory. This yields a new order two autoequivalence for the Z_2 quotient of the conifold.