MASSLESS FLOWS I: THE SINE-GORDON AND O(n) MODELS

Author:

FENDLEY P.1,SALEUR H.2,ZAMOLODCHIKOV AL. B.3

Affiliation:

1. Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA

2. Department of Physics, University of Southern California, Los Angeles, CA 90089, USA

3. Laboratoire de Physique Mathématique, Université Montpellier 2, Montpellier, France

Abstract

The massless flow between successive minimal models of conformal field theory is related to a flow within the sine-Gordon model when the coefficient of the cosine potential is imaginary. This flow is studied, partly numerically, from three different points of view. First we work out the expansion close to the Kosterlitz-Thouless point, and obtain roaming behavior, with the central charge going up and down in between the UV and IR values of c=1. Next we analytically continue the Casimir energy of the massive flow (i.e. with real cosine term). Finally we consider the lattice regularization provided by the O(n) model in which massive and massless flows correspond to high- and low-temperature phases. A detailed discussion of the case n=0 is then given using the underlying N=2 supersymmetry, which is spontaneously broken in the low-temperature phase. The “index” tr F(−1)F follows from the Painlevé III differential equation, and is shown to have simple poles in this phase. These poles are interpreted as occurring from level crossing (one-dimensional phase transitions for polymers). As an application, new exact results for the connectivity constants of polymer graphs on cylinders are obtained. These results and points of view are used in the following paper to discuss the appropriate exact S matrices and the resulting Casimir energies.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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