Form factors in the massless coset models su(2)_k+1 \otimes su(2)_k /su(2)_2k+1 - Part II

TL;DR

This paper investigates massless flows in coset models using form factors, constructing operators' form factors and estimating conformal weight differences to understand the flow from specific coset models to minimal models.

Contribution

It constructs form factors for operators in massless flows of coset models and estimates conformal weight differences, providing new insights into the operator structure of these flows.

Findings

Constructed form factors for operators flowing to ,2 and ,1 in the IR.

Numerical estimates of conformal weight differences align with theoretical expectations.

Identified UV operators corresponding to specific IR operators.

Abstract

Massless flows from the coset model su(2)_k+1 \otimes su(2)_k /su(2)_2k+1 to the minimal model M_k+2 are studied from the viewpoint of form factors. These flows include in particular the flow from the Tricritical Ising model to the Ising model. By analogy with the magnetization operator in the flow TIM -> IM, we construct all form factors of an operator that flows to \Phi_1,2 in the IR. We make a numerical estimation of the difference of conformal weights between the UV and the IR thanks to the \Delta-sum rule; the results are consistent with the conformal weight of the operator \Phi_2,2 in the UV. By analogy with the energy operator in the flow TIM -> IM, we construct all form factors of an operator that flows to \Phi_2,1. We propose to identify the operator in the UV with \sigma_1\Phi_1,2.