G. Mussardo

S Matrix of the Yang-Lee Edge Singularity in Two-Dimensions

Abstract The deformation by a relevant operator of the simplest, albeit nonunitary, conformal field theory, that of the Yang-Lee edge singularity, is analysed. It is shown that additional conserved currents exist which imply the factorization of the S -matrix, whose form is explicitly derived. The spectrum contains a single particle. It is proved that any such theory with only one particle must necessarily be nonunitary.

Boundary energy and boundary states in integrable quantum field theories

Abstract We study the ground-state energy of integrable 1 + 1 quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new “R-channel TBA”, where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S -matrix of O ( n ) and minimal models.

Off-critical statistical models: Factorized scattering theories and bootstrap program

Abstract We analyze those integrable statistical systems which originate from some relevant perturbations of the minimal models of conformal field theories. When only massive excitations are present, the systems can be efficiently characterized in terms of the relativistic scattering data. We review the general properties of the factorizable S -matrix in two dimensions with particular emphasis on the bootstrap principle. The classificati on program of the allowed spins of conserved currents and of the non-degenerate S -matrices is discussed and illustrated by means of some significant examples. The scattering theories of several massive perturbations of the minimal models are fully discussed. Among them are the Ising model, the tricritical Ising model, the Potts models, the series of the non-unitary minimal models M 2,2n +3 , the non-unitary model M 3,5 and the scaling limit of the polymer system. The ultraviolet limit of these massive integrable theories can be exploited by the thermodynamics Bethe ansatz, in particular the central charge of the original conformal theories can be recovered from the scattering data. We also consider the numerical method based on the so-called conformal space truncated approach which confirms the theoretical results and allows a direct measurement of the scattering data, i.e. the masses and the S -matrix of the particles in bootstrap interaction. The problem of computing the off-critical correlation functions is discussed in terms of the form-factor approach.

Integrable Systems Away from Criticality: The Toda Field Theory and S Matrix of the Tricritical Ising Model

Abstract The tricritical Ising model, considered as coset construction with the exceptional group E 7 , is analyzed away from criticality. The additional conserved currents of the corresponding Toda system imply the factorization of the S -matrix, explicitly computed. We discuss the origin of higher-order poles on the physical sheet of the scattering amplitudes and their relevance to the three-point couplings of the theory.

On the operator content of the sinh-Gordon model

Abstract We classify the operator content of local hermitian scalar operators in the sinh-Gordon 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 F2n and F2n−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 ekgφ. 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).

Form factors for integrable lagrangian field theories, the sinh-Gordon model

Using Watsons and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field

Quantum Quenches in Integrable Field Theories

\phi(x)

Scattering theory and correlation functions in statistical models with a line of defect

and the stress-energy tensor

Form-factors of Descendent Operators in Perturbed Conformal Field Theories

T_{\mu\nu}(x)

The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc

of Sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of