Semiclassical approach to form factors in the sinh-Gordon model

Abstract

Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter $b\sim {\hslash }^{1/2}$ in the background of a radial classical solution, which describes a heavy exponential operator placed at the origin. For this purpose we use a generalization of the radial quantization scheme, well known for a massless boson field. We introduce and study new special functions which generalize the Bessel functions and have a nice interpretation in the Tracy-Widom theory of the Fredholm determinant solutions of the classical sinh-Gordon model. Form factors of the exponential operators in the leading order are completely determined by the classical solutions, while form factors of the descendant operators contain quantum corrections even in this approximation. The construction of descendant operators in two chiralities requires renormalizations similar to those encountered in the conformal perturbation theory.

v2: Appendix A partially rewritten; misprints corrected; v3: minor changes in Introduction; references added; v4: minor misprints and stylistic issues corrected; v5: misprints in eqs. (2.2), (4.33), (B.1a), (B.1c) and a few minor misprints corrected

References in corpus (6)

• How instanton combinatorics solves Painlevé VI, V and III's
• On one-point functions for sinh-Gordon model at finite temperature
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Reflection relations and fermionic basis
• Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities
• On form factors and Macdonald polynomials