Model of the N -quark potential in SU ( N ) gauge theory using gauge-string duality

Abstract

We use gauge-string duality to model the N -quark potential in pure Yang-Mills theories. For SU (3), the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the ∆-law at short distances and the Y-law at long distances.

Some aspects of three-quark potentials

“…In this paper we continue a series of studies [17,18] devoted to the three-quark potentials within a five (ten)-dimensional effective string theory. The model we are developing represents a kind of soft wall model of [19], where the violation of conformal symmetry is manifest in the background metric [20].…”

“…As a warmup, let us give a derivation of the three-quark potential in the case when the quarks are at the vertices of an equilateral triangle of length L [18]. To this end, we consider the configuration shown in Figure 2.…”

“…A simple estimate using (2.11) and the fitted value of κ shows that [18] 15) where α QQ is a coefficient in front of the Coulomb term of the quark-antiquark potential [22]. Explicitly, it is given by α QQ = (2π…”

“…Subsequent work made it clear that the model should be taken seriously, particular in the context of consistency with the lattice [23] and quarkonium spectrum [24]. Another instance of perfect consistency between the model [18] and the lattice calculations [9,11,12] is the three-quark potential obtained on an equilateral triangle. In addition, the model also reproduces one of the hybrid potentials of [25].…”

Color screening masses from string models

“…This ansatz is quite successful because it allows us to describe the lattice results for the expectation value of a baryonic Wilson loop by using one free parameter which is m [12]. In the presence of an external gauge field, we extend the action by adding a coupling to A t :…”