On the third level descendent fields in the Bullough–Dodd model and its reductions

P Baseilhac,M Stanishkov

doi:10.1016/s0370-2693(03)00007-8

P Baseilhac, M Stanishkov

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https://doi.org/10.1016/s0370-2693(03)00007-8

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Journal: Physics Letters B	Publication Date: Jan 15, 2003
Citations: 4	License type: cc-by

Affiliation: Kyoto University, Ewha Womans University

Abstract

Exact vacuum expectation values of the third level descendent fields 〈(∂ϕ)3(∂̄ϕ)3eaϕ〉 in the Bullough–Dodd model are proposed. By performing quantum group restrictions, we obtain 〈L−3L̄−3Φlk〉 in perturbed minimal conformal field theories.

Highlights

In 2-D integrable quantum field theories which can be considered as conformal field theories (CFTs) perturbed by a relevant operator, two-point correlation functions are complicated objects to study
Using operator product expansion (OPE) in the short-distance limit one can reduce down their expression in terms of vacuum expectation values (VEVs) of local fields
The purpose of this letter is to provide an exact expression for the VEV of the third level descendent fields in the BD model, in order to complete the short-distance expansion of the two-point function calculated in [6]

Summary

Introduction

In 2-D integrable quantum field theories which can be considered as conformal field theories (CFTs) perturbed by a relevant operator, two-point correlation functions are complicated objects to study. The purpose of this letter is to provide an exact expression for the VEV of the third level descendent fields (next to leading order in the UV limit of the two-point function) in the BD model, in order to complete the short-distance expansion of the two-point function calculated in [6]. Perturbed by the operator Φpert ∈ {Φ12, Φ21, Φ15} can be obtained by a quantum group (QG) restriction of imaginary Bullough-Dodd model [8, 9, 10, 11] with special values of the coupling. We denote respectively Φ12, Φ21 and Φ15 as specific primary operators of the unperturbed minimal model Mp/p′ and introduce the parameter λ which characterizes the strength of the perturbation. Using this correspondence and the previous VEVs in the BD model, we will deduce 0s|L−3L−3Φlk|0s in the perturbed minimal model (2)

VEVs of the third level descendent fields

Application to perturbed conformal field theories

Conclusion