Asymptotic Freedom in a String Model of High Temperature QCD

TL;DR

This paper explores the phase transition in a string model of high-temperature QCD, showing that the string's winding states mimic QCD string behavior and deriving a relation between string and QCD couplings.

Contribution

It provides a novel computation of the free energy of an interacting rigid string at finite temperature and establishes a precise link between string parameters and QCD coupling constants.

Findings

Winding state mass matches high-temperature QCD string behavior

Derived relation between string and QCD coupling constants

Reproduces the asymptotic beta function of QCD

Abstract

Recently we have shown that a phase transition occurs in the leading and sub-leading approximation of the large N limit in rigid strings coupled to long range Kalb-Ramond interactions. The disordered phase is essentially the Nambu-Goto-Polyakov string theory while the ordered phase is a new theory. In this letter we compute the free energy per unit length of the interacting rigid string at finite temperature. We show that the mass of the winding states solves that of QCD strings in the limit of high temperature. We obtain a precise identification of the QCD coupling constant and those of the interacting rigid string. The relation we obtain is $Ng_{QCD}^2=({4\pi^2(D-2)\over 3})^2{1\over 3\kappa}$ where $\kappa={Dt\alpha\over\pi\mu_{c}}$ is the ratio of the extrinsic curvature coupling constant t, the Kalb-Ramond coupling constant $\alpha$, and the critical string tension $\mu_{c}$. The running beta function of $\kappa$ reproduces correctly the asymptotic behaviour of QCD.