Massless Flows II: the exact S-matrix approach

TL;DR

This paper investigates the spectrum and S-matrices of massless flows between minimal models and sine-Gordon models, confirming the c-function flow using the thermodynamic Bethe ansatz and revealing unique behaviors in non-unitary cases.

Contribution

It provides exact S-matrices for massless kinks in minimal models and analyzes their flows, extending understanding of non-perturbative aspects of these conformal field theories.

Findings

Exact S-matrices describe massless kink scattering.

The c-function flows correctly between theories as conjectured.

Unusual behavior observed in non-unitary sine-Gordon models.

Abstract

We study the spectrum, the massless S-matrices and the ground-state energy of the flows between successive minimal models of conformal field theory, and within the sine-Gordon model with imaginary coefficient of the cosine term (related to the minimal models by ``truncation''). For the minimal models, we find exact S-matrices which describe the scattering of massless kinks, and show using the thermodynamic Bethe ansatz that the resulting non-perturbative c-function (defined by the Casimir energy on a cylinder) flows appropriately between the two theories, as conjectured earlier. For the non-unitary sine-Gordon model, we find unusual behavior. For the range of couplings we can study analytically, the natural S-matrix deduced from the minimal one by ``undoing'' the quantum-group truncation does not reproduce the proper c-function with the TBA. It does, however, describe the correct properties of the model in a magnetic field.