Abstract
We establish and develop a correspondence between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional \U0001d4a9 = 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.
Highlights
Quantum field theories with supersymmetry have been a staple of research in fundamental Physics for more than half a century
We 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
Summary
Quantum field theories with supersymmetry have been a staple of research in fundamental Physics for more than half a century. In our use of Kashiwara crystals, we have relied considerably on the recent presentation by Bump and Schilling [35] where, based on the results of Kashiwara, and on the later work by Stembridge [36], an axiomatic combinatorial approach to the construction of crystal bases associated to quantum-deformed enveloping algebras of finite-dimensional Lie algebras is developed. This approach can be of significant advantage when there is already a background or familiarity with the combinatorics of Young tableaux, such as in the construction of the irreducible representations of the symmetric and general linear groups, by means of such tableaux.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
