Integrability from supersymmetric duality: a short review

Abstract

Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In this brief review, we discuss a program of constructing integrable lattice spin models with the nearest neighbor interaction using methods inspired by the supersymmetric gauge theory computations, called gauge/YBE correspondence. After a brief introduction to the topic, we review some recent examples of this correspondence and the role of special functions and symmetries. Finally, we discuss future directions of research.

Application of GIS in Solid Waste Management in Gara Garayev Avenue, Nizami district, Baku city, Azerbaijan.

“…The equality (21) has an interpretation as the inversion relation 9 for exactly solvable lattice spin model introduced in [16,18]. In particular, this observation can be used [51] for a better understanding of the correspondence [42,52,53,54] between supersymmetric gauge theories and integrable models of statistical mechanics.…”

On Bailey pairs for $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on $$ {S}_b^3/{\mathbb{Z}}_r $$

“…In recent years, the remarkable concept of hypergeometric identities sits at the intersection of diverse studies such as exact results in supersymmetric gauge theories [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and their mathematical structures interacting with various fields in mathematics, see, e.g., [15][16][17][18], star-triangle relation (Yang-Baxter equation) [19][20][21][22][23][24][25][26][27][28] or star-star relation [29][30][31][32] for spin lattice models, knot theory [33], pentagon identities [33][34][35][36][37][38][39][40][41], Bailey pairs [23,[42][43][44][45], quantum algebras [28,…”

A comment on the solutions of the generalized Faddeev-Volkov model

“…Some studies employ the gauge/YBE correspondence to connect supersymmetric gauge theories and integrable lattice models of statistical mechanics, e.g. [1][2][3][4][5][6][7][8][9][10][11], whereas others use special functions and algebraic techniques, see, e.g. [12][13][14][15][16][17].…”