Abstract
We establish and develop a correspondence 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.
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Santilli, L., Tierz, M. Crystal bases and three-dimensional 𝒩 = 4 Coulomb branches. J. High Energ. Phys. 2022, 73 (2022). https://doi.org/10.1007/JHEP03(2022)073
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DOI: https://doi.org/10.1007/JHEP03(2022)073
Keywords
- Supersymmetric Gauge Theory
- Field Theories in Lower Dimensions
- Differential and Algebraic Geometry