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Modern Physics Letters A

ULTRAVIOLET BEHAVIOR OF THE INTEGRABLE OFF-CRITICAL NON-UNITARY SERIES M3/q

Philippe Christe, Marcio Jose Martins

Published Oct 20, 1990• 30 citations
Publisher

Abstract

We discuss the ultraviolet behavior of the non-unitary M3/q (q = 5, 7) minimal models perturbed by the operator ϕ13. The Thermodynamic Bethe Ansatz is used to compute the central charge and the next higher order corrections in the high temperature expansion of the finite volume ground state energy. The results are in perfect agreement with perturbative calculations. Generalizations of these results are commented on.

DOI
10.1142/s0217732390002493

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We discuss the ultraviolet behavior of the non-unitary M3/q (q = 5, 7) minimal models perturbed by the operator ϕ13. The Thermodynamic Bethe Ansatz is used to compute the central charge and the next higher order corrections in the high temperature expansion of the finite volume ground state energy. The results are in perfect agreement with perturbative calculations. Generalizations of these results are commented on.
By using the thermodynamic Bethe ansatz approach, we give evidence of the existence of both massive and massless behaviors for the ϕ2,1 perturbation of the M3,5 nonunitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviors correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of nonunitary minimal models Mp,2p±1, perturbed by their least relevant operator, lead to a cascade of flows similar to that of unitary minimal models perturbed by ϕ1,3. Various aspects and generalizations of this phenomenon and the links with the Izergin–Korepin model are discussed.
Abstract We study the thermodynamic Bethe ansatz (TBA) equations for pure T T ¯ perturbations of some simple integrable quantum field theories with a single bosonic or fermionic particle, in particular the massive sinh-Gordon model and its ultraviolet (UV) limit which is a deformation of the conformally invariant free massless boson. Whereas the TBA equations for T T ¯ deformations of massive theories are in principle known, the TBA equations we propose for the deformations of conformal field theories are relatively new and require a special factorization in rapidity variables of the CDD factor for the scattering of the massless particles. The latter TBA equations can be solved exactly and reproduce the known results for the ground state energy on a cylinder of circumference R which were previously obtained using different methods based for instance on the Burgers differential equation. Special attention is paid to the c -theorem in this context which is discussed in some detail. For positive infra-red central charge c IR , for flows consistent with the c -theorem the ground state energy develops a (previously known) square-root singularity toward the UV, which strongly suggests the theories are UV incomplete in these physically important cases. We suggest that the singularity indicates a tachyonic vacuum instability. Other cases with c IR < 0 do not have this singularity are interpreted as being UV complete with c UV = 0. We extend our results to a continuously variable c IR by introducing a chemical potential and suggest this as a possible toy model for the T T ¯ perturbed Liouville theory.
We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator phi2,1\\phi_{2,1}phi2,1​. This operator has conformal dimensions (7/16,7/16)(7/16,7/16)(7/16,7/16) and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.