Low Energy Effective Theory of QCD at High Isospin Chemical Potential

TL;DR

This paper derives a low energy effective theory for high isospin density QCD with two massless flavors, calculates the low energy constants, and predicts the critical temperature for deconfinement transition as a function of isospin chemical potential.

Contribution

It provides the first calculation of low energy constants for the pure Yang-Mills effective theory of high isospin QCD, enabling predictions of the deconfinement temperature.

Findings

Calculated low energy constants for the effective Yang-Mills theory.

Predicted the scaling of the critical temperature with isospin chemical potential.

Established a basis for future lattice QCD comparisons.

Abstract

The goal of this paper is to arrive at a low energy effective theory of QCD with two massless flavors of quarks at very high isospin density and zero baryon density. In a seminal paper by Son and Stephanov in the year 2001, it was conjectured that the low energy dynamics of QCD with two light flavors at asymptotically high isospin density was described by that of a pure Yang-Mills effective Lagrangian. Since the existence of a first order deconfinement phase transition with increasing temperature is a feature of every pure SU(N) Yang-Mills theory with N greater than or equal to 3, the regime considered in this paper is also expected to exhibit a first order deconfinement phase transition with increasing temperature. However, the low energy constants(LEC) of this pure Yang-Mills theory have not been calculated till date. We calculate the LEC s for this effective theory which in turn enables us to calculate the critical temperature of the deconfinement transition as a function of the isospin chemical potential $\mu_I$.The scaling of the critical temperature as a function of the isospin chemical potential that we find in this paper can be compared with future lattice calculations at finite isospin density.