2021/11/30 by Leonardo Santilli, Miguel Tierz
Mathematics · Physics and Astronomy · #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Axiom #Black Holes and Theoretical Physics #Computer science #Coulomb #Crystal (programming language) #Equivalence (formal languages) #Gauge theory #Geometry #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Quiver #Theoretical physics #hep-th #math-ph #math.AG #math.CO #math.MP
paper · pdf · doi:10.1007/jhep03(2022)073
published as J. High Energ. Phys. 2022, 73 (2022) · ii+60 pages, many figures. v2: minor improvements. v3: clarifications and references added, published version
openalex publication_date 2022/03/01 · arxiv created 2022/03/22 · arxiv updated 2022/03/24 · openalex created_date 2022/04/03 · openalex updated_date 2026/06/22
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.