Expectation values of descendent fields in the Bullough-Dodd model and related perturbed conformal field theories

TL;DR

This paper computes exact vacuum expectation values of certain descendent fields in the Bullough-Dodd model and related perturbed conformal field theories, revealing their relation to free energy and extending known results.

Contribution

It provides explicit formulas for expectation values of second level descendent fields and connects them to perturbed minimal conformal field theories using quantum group restrictions.

Findings

Exact expectation value of $<T\overline T>$ proportional to free energy squared

Derived vacuum expectation values for second level descendent fields

Extended results to $ ext{Phi}_{12}$, $ ext{Phi}_{21}$, and $ ext{Phi}_{15}$ perturbed minimal models

Abstract

The exact vacuum expectation values of the second level descendent fields $<(\partial\phi)^2({\overline\partial}\phi)^2e^{a\phi}>$ in the Bullough-Dodd model are calculated. By performing quantum group restrictions, we obtain $<L_{-2}{\overline L}_{-2}{\Phi}_{lk}>$ in the $\Phi_{12}$, $\Phi_{21}$ and $\Phi_{15}$ perturbed minimal CFTs. In particular, the exact expectation value $<T{\overline T}>$ is found to be proportional to the square of the bulk free energy.