Resonances in sinh and sineGordon models and higher equations of motion in Liouville theory
Abstract
The notion of operator resonances was previously introduced by Al Zamolodchikov within the framework of the conformal perturbation theory. The resonances are related to logarithmic divergences of integrals in the perturbation expansion, and manifest themselves in poles of the correlation functions and form factors of local operators considered as functions of conformal dimensions. The residues of the poles can be computed by means of some operator identities. Here, we study the resonances in the Liouville, sinh and sineGordon models, considered as perturbations of a massless free boson. We show that the wellknown higher equations of motion discovered by Al Zamolodchikov in the Liouville field theory are nothing but resonance identities for some descendant operators. The resonance expansion in the vicinity of a resonance point provides a regularized version of the corresponding operators. We try to construct the corresponding resonance identities and resonance expansions in the sinh and sineGordon theories. In some cases it can be done explicitly, but in most cases we are only able to obtain a general form so far. We show nevertheless that the resonances are perturbatively exact, which means that each of them only appears in a single term of the perturbation theory.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2012
 DOI:
 10.1088/17518113/45/45/455403
 arXiv:
 arXiv:1111.2547
 Bibcode:
 2012JPhA...45S5403L
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 22 pages, no figures