FORM FACTORS AND CORRELATION FUNCTIONS OF THE STRESS-ENERGY TENSOR IN MASSIVE DEFORMATION OF THE MINIMAL MODELS (E_n)₁⊗ (En)₁/(E_n)₂

Abstract

The magnetic deformation of the Ising Model, the thermal deformations of both the Tricritical Ising Model and the Tricritical Potts Model are governed by an algebraic structure based on the Dynkin diagram associated to the exceptional algebras E n (respectively for n = 8, 7, 6). We make use of these underlying structures as well as of the discrete symmetries of the models to compute the matrix elements of the stress-energy tensor and its two-point correlation function by means of the spectral representation method.

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

“…However, the convergence property of the truncated series is much better [8] and as a matter of fact it neatly approximates the correlator up to the region r ∼ ξ, as has been checked in several examples (see, for instance [10,11,14,45,46,47]). Therefore the truncated spectral series is assumed to estimate the integral I 2 (R) in eq.…”

“…These amplitudes have been computed in [21,22] and their concise expressions can be found in Table 2 of ref. [47]. The exact mass spectrum of the excitations can be extracted from the pole structure of the S matrices (see Table 9).…”

“…Their calculations, together with some subtleties which occur in this case, are discussed in Appendix D. The Form Factors of the operator ǫ(x), which plays the role of the trace of the stress-energy tensor for this deformation, were computed in ref. [47]. The above strategy has been applied for the estimation of all the correlators.…”

Analytic properties of the free energy: the tricritical Ising model

“…(see [28] where this property is exploited for the computation of the matrix elements of the energy-momentum tensor as well as of its two-point correlation function). The tricritical Ising model is also the simplest example of superconformal field theory [29]: its Hilbert space contains a finite number of irreducible representations of the super-Virasoro algebra (the antiholomorphic part is omitted)…”

Universal ratios of the renormalization group

“…In our calculation we have only insert into the spectral representations the one-particle and two-particle FF, computed according to the analysis of ref. [28,29].…”