Paolo Grinza

Decay of particles above threshold in the Ising field theory with magnetic field

Abstract The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles A i ( i = 1 , … , 8 ) with different masses. The heaviest five lie above threshold and owe their stability to integrability. We use form factor perturbation theory to compute the decay widths of the first two particles above threshold when integrability is broken by a small deviation from the critical temperature. The lifetime ratio t 4 / t 5 is found to be 0.233; the particle A 5 decays at 47% in the channel A 1 A 1 and for the remaining fraction in the channel A 1 A 2 . The increase of the lifetime with the mass, a feature which can be expected in two dimensions from phase space considerations, is in this model further enhanced by the dynamics.

On the finite size corrections of anti-ferromagnetic anomalous dimensions in Script N = 4 SYM

Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. anti-ferromagnetic) and immediately lower anomalous dimensions of scalar operators in = 4 SYM. In specific, multi-loop corrections are computed in the SU(2) operator subspace, whereas in the general SO(6) case only one loop calculations have been finalised. In these cases, the leading finite size corrections are given by means of explicit formul? and compared with the exact numerical evaluation. In addition, the method here proposed is quite general and especially suitable for numerical evaluations.

Potts correlators and the static three-quark potential

We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2 + 1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a Δ-type law at short distances and a Y-type law at large distances.

Form factors in the massless coset models su(2)k+1⊗su(2)k/su(2)2k+1su(2)k+1⊗su(2)k/su(2)2k+1: Part II

Abstract Massless flows between the coset model su ( 2 ) k + 1 ⊗ su ( 2 ) k / su ( 2 ) 2 k + 1 and the minimal model M k + 2 are studied from the viewpoint of form factors. These flows include, in particular, the flow between the tricritical Ising model and the Ising model. Form factors of the trace operator with an arbitrary number of particles are constructed, and numerical checks on the central charge are performed with four-particle contribution. Large discrepancies with respect to the exact results are observed in most cases.

Form Factors in the Massless Coset Models su(2) k+1 su(2) k /su(2) 2k+1 : Part II

Massless flows from the coset model su(2)_k+1 \otimes su(2)_k /su(2)_2k+1 to the minimal model M_k+2 are studied from the viewpoint of form factors. These flows include in particular the flow from the Tricritical Ising model to the Ising model. By analogy with the magnetization operator in the flow TIM -> IM, we construct all form factors of an operator that flows to \Phi_1,2 in the IR. We make a numerical estimation of the difference of conformal weights between the UV and the IR thanks to the \Delta-sum rule; the results are consistent with the conformal weight of the operator \Phi_2,2 in the UV. By analogy with the energy operator in the flow TIM -> IM, we construct all form factors of an operator that flows to \Phi_2,1. We propose to identify the operator in the UV with \sigma_1\Phi_1,2.