Correlation Functions of The Tri-critical 3-states Potts Model

TL;DR

This paper analyzes the correlation functions of the tri-critical 3-states Potts model using conformal algebra invariants, bootstrap methods, and integral representations to determine operator algebra constants.

Contribution

It constructs the Z₃ invariants fusion rules for the (D₄,A₆) conformal algebra and compares bootstrap and integral approaches to find structure constants.

Findings

Fusion rules for the (D₄,A₆) algebra established

Correlation functions expressed via bootstrap and integrals compared

Operator algebra constants determined

Abstract

We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the bootstrap approach, and in the other hand, they are written in term of integral representation of the conformal blocks. By comparing both the expressions, one can determine the structure constantes of the operator algebra.