Quantum Deformations from Toric Geometry

TL;DR

This paper introduces a novel method combining toric geometry calculations with gauge theory to compute quantum corrections to the chiral ring relations in specific quiver gauge theories, exemplified by the del Pezzo 2 case.

Contribution

It develops a new approach linking toric geometry deformations with quantum gauge theory corrections, providing a geometric understanding of IR dynamics.

Findings

Toric geometry calculations match gauge theory quantum corrections.

Derived the quantum deformations of the del Pezzo 2 vacuum moduli space.

Extended the method to other examples in an appendix.

Abstract

We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and quantum deformations to the vacuum moduli space using Affleck-Dine-Seiberg superpotential arguments. Then we calculate the versal deformation to the corresponding toric geometry using a method due to Altmann, and show that the result is equivalent to the deformation calculated using gauge theory. In an appendix we will apply this technique to a few other examples. This is a new method for understanding the infrared dynamics of certain quiver gauge theories.