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High Energy Physics - Theory

arXiv:2111.05206 (hep-th)
[Submitted on 9 Nov 2021 (v1), last revised 22 Mar 2022 (this version, v3)]

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

Authors: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.
Comments: ii+60 pages, many figures. v2: minor improvements. v3: clarifications and references added, published version
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Combinatorics (math.CO)
Cite as: arXiv:2111.05206 [hep-th]
  (or arXiv:2111.05206v3 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2111.05206
Journal reference: J. High Energ. Phys. 2022, 73 (2022)
Related DOI: https://doi.org/10.1007/JHEP03%282022%29073

Submission history

From: Leonardo Santilli [view email]
[v1] Tue, 9 Nov 2021 15:32:36 UTC (69 KB)
[v2] Tue, 11 Jan 2022 08:53:07 UTC (69 KB)
[v3] Tue, 22 Mar 2022 19:09:52 UTC (71 KB)
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