On the operator content of the sinh-Gordon model

Abstract

We classify the operator content of local hermitian scalar operators in the SinhGordon model by means of independent solutions of the form-factor bootstrap equations. The corresponding linear space is organized into a tower-like structure of dimension n for the form factors F 2n and F 2n−1 . Analyzing the cluster property of the form factors, a particular class of these solutions can be identified with the matrix elements of the operators e kgφ . We also present the complete expression of the form factors of the elementary field φ(x) and the trace of the energy-momentum tensor Θ(x).

Sine-Gordon multisoliton form factors in finite volume

“…This expectation was confirmed in many cases by explicit comparison of the space of solutions to the spectrum of local operators as described by the ultraviolet limiting conformal field theory [8,9,10,11,12,13,14,15]; the mathematical foundation is provided by the local commutativity theorem stating that operators specified by solutions of the form factor bootstrap are mutually local [5]. Another important piece of information comes from correlation functions.…”

Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

“…Indeed, N -particle matrix elements with vanishing residues on the bound state and kinematical poles are themselves initial conditions of kernel solutions which in a linear combination give no contribution for n < N . Enumerating the kernel solutions is then essential for counting the independent solutions of the form factor equations, as originally observed in [26].…”

Universal amplitude ratios of the renormalization group: Two-dimensional tricritical Ising model

“…However, even in the more favorable case of integrable theories, it may occur that the determination of the one-particle FF can be only obtained by a numerical approach. Despite the existence of a manageable set of recursive equations which link the various n-particle Form Factors in the integrable models, the solutions of these recursive equations need an initial input which cannot be often obtained even by employing the cluster property of the Form Factors [43,54,55]. Under this circumstance one has to necessarily resort to other methods for obtaining the one-particle FF's and the TCSA may help in this respect.…”