Potts correlators and the static three-quark potential

Abstract

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 ∆ type law at short distances and a Y type law at large distances.

Universal behaviour of interfaces in 2d and dimensional reduction of Nambu–Goto strings

“…We retrieve in this way the 2d expression proportional to K 1 (mR) which we propose in this paper. This dimensional reduction is the exact analogue for the interface boundary conditions of the dimensional reduction from Polyakov loop correlators to spinspin correlators studied in [14,15]. A non trivial consistency test of this correspondence is that the relation which links the 2d mass m with the 3d string tension σ is the same in the case of interfaces and of Polyakov loops.…”

Glueball masses in(2+1)-dimensional anistropic weakly-coupled Yang-Mills theory

“…Another recent application of exact form factors to the (2 + 1)-dimensional SU(2) gauge theory is reference [13], in which form factors of the two-dimensional Ising model [14] are used to find the profile of the electric string near the high-temperature deconfining transition, assuming the Svetitsky-Yaffe conjecture [15].…”

Integrable structures in LGTs near the deconfinement transition

“…In sect. 2 we report on the study of the baryon (three-quark) potential in the 3D SU (3) LGT using the three-spin correlation function of the 2D 3-state Potts model [5]. Sect.…”

“…Sect. 3 is devoted to the study of the behaviour of the flux tube thickness in the 2D SU (2) LGT via the corresponding 2D Ising model [9]. Finally, in sect.…”

“…The appearance of the Steiner point is quite natural in such a framework (even if completely non-trivial), and it is strongly related to the integrable structure of the model. Here we quote the final result (leading and sub-leading orders) in the case of an equilateral triangle of side R (see [5] for details)…”