Integrable Structure of $5d$ $\mathcal{N}=1$ Supersymmetric Yang-Mills and Melting Crystal

TL;DR

This paper explores the integrable structure linking 5-dimensional N=1 supersymmetric Yang-Mills theory with melting crystal models, revealing a deep mathematical connection through loop operators and partition functions.

Contribution

It demonstrates that the generating functions of loop operators in 5d N=1 SYM correspond to melting crystal partition functions, establishing a new integrable structure link.

Findings

For U(1) theory, the correlation functions match melting crystal partition functions.

Identifies a common integrable structure between 5d SYM and melting crystal models.

Provides a new perspective on the mathematical structure of supersymmetric gauge theories.

Abstract

We study loop operators of $5d$ $\mathcal{N}=1$ SYM in $\Omega$ background. For the case of U(1) theory, the generating function of correlation functions of the loop operators reproduces the partition function of melting crystal model with external potential. We argue the common integrable structure of $5d$ $\mathcal{N}=1$ SYM and melting crystal model.