Quantum Deformations from Toric Geometry

Details Quantum Deformations from Toric Geometry Quantum Deformations from Toric Geometry

2005-11-03

arxiv.org/abs/hep-th/0511027v3

JHEP 0603:055,2006

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 4 figures, uses axodraw.sty, latex

Scientific paper

10.1088/1126-6708/2006/03/055

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.

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