(Ir)regular singularities and Quantum Field Theory

PUBLICATIONS

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Random Matrices and Gauge theories

Crystal bases and three-dimensional N=4 Coulomb branches

Author(s)

Leonardo Santilli,
Miguel Tierz

Topic

Random Matrices and Gauge theories

Abstract

We establish and develop a bijection between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional N=4 gauge theories. The result holds for simply-laced, non-simply laced and affine quivers. Two equivalent derivations are given in the non-simply laced case, either by application of the axiomatic rules or by folding a simply-laced quiver. We also study the effect of turning on real masses and the ensuing simplification of the crystal. We present a multitude of explicit examples of the equivalence. Finally, we put forward a correspondence between infinite crystals and Hilbert spaces of theories with isolated vacua.

Year

2021

Reference

L. Santilli and M. Tierz. “Crystal bases and three-dimensional N=4 Coulomb branches.”

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