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arXiv · 2111.05206

Crystal bases and three-dimensional $ \mathcal{N}=4 $ Coulomb branches

Leonardo Santilli·Miguel Tierz
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Abstract

We establish and develop a correspondence between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional $ \mathcal{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.

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Leonardo Santilli, Miguel Tierz. 2021-11-09. Crystal bases and three-dimensional $ \mathcal{N}=4 $ Coulomb branches. https://doi.org/10.1007/jhep03(2022)073

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