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

The exact vacuum expectation values of the second level descendent fields $<(\partialϕ)^2({\overline\partial}ϕ)^2e^{aϕ}>$ in the Bullough-Dodd model are calculated. By performing quantum group restrictions, we obtain $<L_{-2}{\overline L}_{-2}Φ_{lk}>$ in the $Φ_{12}$, $Φ_{21}$ and $Φ_{15}$ 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.

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