Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories

TL;DR

This paper derives exact expectation values of exponential fields in the Bullough-Dodd model using reflection relations and applies these results to compute expectation values in perturbed minimal conformal field theories, including Liouville theory connections.

Contribution

It provides explicit formulas for expectation values of primary operators in perturbed minimal models, linking integrable quantum field theories with conformal field theory results.

Findings

Derived exact expectation values in the Bullough-Dodd model.

Proposed explicit expressions for primary operators in perturbed minimal CFTs.

Presented results for Phi_{1,5} perturbed minimal models.

Abstract

Exact expectation values of the fields e^{a\phi} in the Bullough-Dodd model are derived by adopting the ``reflection relations'' which involve the reflection S-matrix of the Liouville theory, as well as special analyticity assumption. Using this result we propose explicit expressions for expectation values of all primary operators in the c<1 minimal CFT perturbed by the operator \Phi_{1,2} or Phi_{2,1}. Some results concerning the $\Phi_{1,5}$ perturbed minimal models are also presented.