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 $<(\partial \varphi {)}^2(\overline{\partial }\varphi {)}^2{e}^{a\varphi }>$ 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.

17 pages, LaTeX file with amssymb, v2:references added. To appear in Nucl. Phys. B

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