Modern Physics Letters A

INTERACTING BOSONIC MODELS AND THEIR SOLUTION

RON COHEN, Doron Gepner

Published Aug 10, 1991• 8 citations

Abstract

A family of interacting bosonic models is studied. A picture is suggested where each such conformal field theory is tensored with a conjugate one to give a free bosonic theory. It is shown that the lattice of the bosonic theory is determined in each case, and how the spectrum and correlation functions can be calculated. It is explained how flat directions can arise in such theories, allowing for an exact solution for a family of parameters. A large class of examples is discussed in detail. It is shown that for any rational value of the central charge c ≥ 3 there is an infinite number of distinct rational N = 2 theories which can be contracted by this method.

DOI: 10.1142/s0217732391002487

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Modern Physics Letters A

INTERACTING BOSONIC MODELS AND THEIR SOLUTION

RON COHEN, Doron Gepner

Published Aug 10, 1991• 8 citations

Publisher

Abstract

DOI: 10.1142/s0217732391002487

Related papers

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n

point functions. The Hilbert space of the conformal fields in two dimensions is formally constructed through the \textit{representation theory of Virasoro algebra}. Accordingly, the reducible and irreducible \textit{Verma modules} are specified. Due to the unitarity requirement of the Hilbert space, the famous \textit{Kac determinant} is introduced to obtain constraints on the inner products of the Verma modules, whence on the \textit{conformal weights} and the central charge. The decoupling of the \textit{null states} from rest of the their conformal families is used to obtain \textit{fusion rules} of the families. The \textit{Kac table} for the constrained conformal weights is constructed, and its analysis under the requirement of unitarity leads to the identification of the \textit{minimal models}. The correspondence between the discrete statistical systems at criticality and the minimal models is studied, where special attention is given on the \textit{Ising model}.

H_3^+

model, and the

SU_2

and

\widetilde{SL}_2(\mathbb{R})

WZW models. We also discuss relations between some of these models, and limits of these models when the central charge and/or conformal dimensions tend to particular values.