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 〈(∂ϕ) 2( ∂ ̄ ϕ) 2e aϕ〉 in the Bullough–Dodd model are calculated. By performing quantum group restrictions, we obtain 〈L −2 L ̄ −2Φ lk〉 in the Φ 12, Φ 21 and Φ 15 perturbed minimal CFTs. In particular, the exact expectation value 〈T T ̄ 〉 is found to be proportional to the square of the bulk free energy.