Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model

TL;DR

The paper investigates how the topological $\theta$-dependence in QCD evolves across the confinement–deconfinement transition in the large-$N$ limit, using both holographic QCD and a low-energy $\eta'$-driven effective theory. It shows that at high temperature the theory admits a dilute instanton gas with $\theta$-dependence $\sim e^{-\gamma N}\cos(\theta)$, while below a critical temperature $T_c$ the instanton expansion breaks down and the relevant degrees of freedom become instanton quarks with fractional topological charges $\pm 1/N$, described by a sine-Gordon Lagrangian whose dual Coulomb-gas representation makes the topological content transparent. The analysis yields a concrete estimate for $T_c$ (approximately $0.53\Lambda_{QCD}$ in Pauli–Villars scheme) and, for small chemical potential, a predictable $T_c(\mu)$ line; it also connects to holographic D0-brane physics and to lattice indications of a sharp $\theta$-driven transition. Overall, the work proposes a cohesive large-$N$ picture where confinement arises from a plasma of fractionally charged constituents, with the $\eta'$ field playing the central role in mediating topological interactions.

Abstract

In the holographic model of QCD, theta dependence sharply changes at the point of confinement deconfinement phase transition. In large N QCD such a change in theta behavior can be related to the breakdown of the instanton expansion at some critical temperature T_c. Associating this temperature with confinement-deconfinement phase transition leads to the description of the latter in terms of dissociation of instantons into the fractionally charged instanton quarks. To elucidate this picture, we introduce the nonvanishing chiral condensate in the deconfining phase and assume a specific lagrangian for the eta' field in the confining phase. In the resulting picture the high temperature phase of the theory consists of the dilute gas of instantons, while the low temperature phase is described in terms of freely moving fractional instanton quarks.