Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Decorating the gauge/YBE correspondence

Erdal Catak, Mustafa Mullahasanoglu

Abstract

In this paper, we aim to study the three-dimensional $\mathcal N=2$ supersymmetric dual gauge theories on $S_b^3/\mathbb{Z}_r$ in the context of the gauge/YBE correspondence. We consider hyperbolic hypergeometric integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation.

Decorating the gauge/YBE correspondence

Abstract

In this paper, we aim to study the three-dimensional supersymmetric dual gauge theories on in the context of the gauge/YBE correspondence. We consider hyperbolic hypergeometric integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation.
Paper Structure (20 sections, 1 theorem, 59 equations, 6 figures)

This paper contains 20 sections, 1 theorem, 59 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Three-dimensional IR dualities
  3. The decoration transformation
  4. SU(2) gauge theory
  5. U(1) gauge theory
  6. Gauge symmetry breaking
  7. Kagome lattice model
  8. The flipping relation
  9. Bailey pairs
  10. The decoration transformations
  11. SU(2) gauge theory
  12. U(1) gauge theory
  13. Flipping relation
  14. SU(2) gauge theory
  15. U(1) gauge theory
  16. ...and 5 more sections

Key Result

Lemma 3.1

When $\alpha(x,m;t,p)$ and $\beta(x,m; t,p)$ form an integral hyperbolic hypergeometric Bailey pair with respect to $t$ and $p$, the novel function as a part of the sequences of functions $\beta'(x,k; t+s,p+q)$ and reparametrized function $\alpha'(x,k;t+s,p+q)$ defined by form an integral hyperbolic hypergeometric Bailey pair with respect to the new parameters $t+s$ and $p+q$.

Figures (6)

  • Figure 1: The decoration transformation.
  • Figure 2: Constructing Kagome lattice from the hexagonal lattice by the use of decoration transformation and the star-triangle relation, respectively.
  • Figure 3: The flipping relation.
  • Figure 4: Lattice for the derivation of the decoration transformation and the flipping relation for IRF-type models.
  • Figure 5: The flipping relation of IRF-type models.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Definition 3.1
  • Lemma 3.1: Bailey Lemma
  • proof