Asymptotic Freedom in a String Model of High Temperature QCD

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.Comment: PHYZZX, 10 page

Phase Transition and Absence Of Ghosts in Rigid QED

Ordinary QED formulated in the Feynman's space-time picture is equivalent to a one dimensional field theory. In the large N limit there is no phase transition in such a theory. In this letter, we show a phase transition does exist in a generalization of QED characterized by the addition of the curvature of the world line (rigidity) to the Feynman's space-time action. The large distance scale of the disordered phase essentially coincides with ordinary QED, while the ordered phase is strongly coupled. Although rigid QED exhibits the typical pathologies of higher derivative theories at the classical level, we show that both phases of the quantum theory are free of ghosts and tachyons. Quantum fluctuations prevent taking the naive classical limit and inherting the problems of the classical theory.Comment: 9 pages, 1 figure, phyzzx, to appear in Phys. Lett. B235 (1994), CINCI3-DEC-9