The 3-state Potts model and Rogers-Ramanujan series

TL;DR

This paper explores the connection between the 3-state Potts model, Rogers-Ramanujan series, and advanced algebraic structures like Virasoro minimal models and $ ext{W}_3$-algebras, revealing new mathematical insights.

Contribution

It demonstrates the appearance of Rogers-Ramanujan series within tensor products of $A_2^{(2)}$-modules using novel algebraic tools.

Findings

Rogers-Ramanujan series appear in tensor products of $A_2^{(2)}$-modules

Utilizes $(5,6)$ Virasoro minimal models and twisted $ ext{W}_3$-algebra modules

Provides a new algebraic framework for understanding the 3-state Potts model

Abstract

We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic $A_2^{(2)}$-modules, previously discovered by the first author in [F]. The key new ingredients are $(5,6)$ Virasoro minimal models and twisted modules for the Zamolodchikov $\WW_3$-algebra.