Semiclassical approach to form factors in the sinhGordon model
Abstract
Form factors in the sinhGordon model are studied semiclassically for small values of the parameter b ~ ħ^{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 TracyWidom theory of the Fredholm determinant solutions of the classical sinhGordon 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2023
 DOI:
 10.1007/JHEP07(2023)157
 arXiv:
 arXiv:2303.11933
 Bibcode:
 2023JHEP...07..157L
 Keywords:

 Field Theories in Lower Dimensions;
 Integrable Field Theories;
 Renormalization and Regularization;
 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 v2: Appendix A partially rewritten