Quantum Deformations from Toric Geometry

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.

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

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Cited by in corpus (14)

• Counting Gauge Invariants: the Plethystic Program
• Sasaki-Einstein Manifolds and Volume Minimisation
• Physics of String Flux Compactifications
• Brane Tilings and Reflexive Polygons
• Gauge Theories at Resolved and Deformed Singularities using Dimers
• Comments on the non-conformal gauge theories dual to Ypq manifolds
• Deformations of Toric Singularities and Fractional Branes
• On Stable Non-Supersymmetric Vacua at the Bottom of Cascading Theories
• Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
• A Quiver of Many Runaways
• Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I
• Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
• Asymptotically conical Calabi-Yau metrics on quasi-projective varieties
• Deformations and D-branes