Rectangular amplitudes,conformal blocks,and applications to loop models |
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Authors: | Roberto Bondesan Jesper L Jacobsen Hubert Saleur |
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Institution: | 1. LPTENS, École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France;2. Institute de Physique Théorique, CEA Saclay, F-91191 Gif-sur-Yvette, France;3. Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France;4. Physics Department, USC, Los Angeles, CA 90089-0484, USA |
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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. B 862 (2012) 553–575]. 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. |
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