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Crystal bases and three-dimensional 𝒩 = 4 Coulomb branches
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 11 March 2022

Crystal bases and three-dimensional 𝒩 = 4 Coulomb branches

  • Leonardo Santilli  ORCID: orcid.org/0000-0002-2497-48681 &
  • Miguel Tierz2,1 

Journal of High Energy Physics volume 2022, Article number: 73 (2022) Cite this article

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A preprint version of the article is available at arXiv.

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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Authors and Affiliations

  1. Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Edifício C6, 1749-016, Campo Grande, Lisboa, Portugal

    Leonardo Santilli & Miguel Tierz

  2. Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Plaza de las Ciencias, 3, 28040, Madrid, Spain

    Miguel Tierz

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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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  • Received: 12 January 2022

  • Accepted: 23 February 2022

  • Published: 11 March 2022

  • DOI: https://doi.org/10.1007/JHEP03(2022)073

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Keywords

  • Supersymmetric Gauge Theory
  • Field Theories in Lower Dimensions
  • Differential and Algebraic Geometry
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