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

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.