Critical values of the Yang–Yang functional in the quantum sine-Gordon model Original Research Article

The critical values of the Yang–Yang functional corresponding to the vacuum states of the sine-Gordon QFT in the finite-volume are studied. Two major applications are discussed: (i) generalization of Fendley–Saleur–Zamolodchikov relations to arbitrary values of the sine-Gordon coupling constant, and (ii) connection problem for a certain two-parameter family of solutions of the Painlevé III equation.