Rectangular amplitudes, conformal blocks, and applications to loop models
Abstract
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks.
Cite
@article{arxiv.1207.7005,
title = {Rectangular amplitudes, conformal blocks, and applications to loop models},
author = {Roberto Bondesan and Jesper Lykke Jacobsen and Hubert Saleur},
journal= {arXiv preprint arXiv:1207.7005},
year = {2012}
}
Comments
46 pages