Confinement/Deconfinement Transition of Large N Gauge Theories with N_f Fundamentals: N_f/N Finite

TL;DR

This paper analyzes large N gauge theories with fundamental matter on compact manifolds, revealing a third-order deconfinement transition and implications for dual string theory and black hole formation.

Contribution

It demonstrates a finite N_f/N ratio in large N gauge theories leads to a third-order deconfinement transition with distinct low and high-temperature phases.

Findings

Identifies a third-order deconfinement phase transition at temperature T_c.

Low-temperature phase dominated by mesons and glueballs with O(N_f^2) free energy.

High-temperature phase characterized by gluons and matter states with O(N^2) free energy.

Abstract

We consider large N zero-coupling d-dimensional U(N) gauge theories, with N_f matter fields in the fundamental representation on a compact spatial manifold S^{d-1} x time, with N_f/N finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature T_c proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of {\cal O} (N^2_f), interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperature (deconfinement) phase has a free energy of order N^2 f (N_f/N, T), which is interpreted as that of a gas of gluons and of fundamental and anti-fundamental matter states. This suggests the existence of a dual string theory, and a transition to a black hole at high temperature.