Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory

TL;DR

This paper extends the understanding of QCD at high isospin density by deriving an effective theory, analyzing the sign problem, and connecting it to random matrix theory, providing insights into phenomena like the Silver Blaze effect.

Contribution

It generalizes QCD to arbitrary flavors at high isospin density, derives effective theories, and maps to known random matrix models to analyze the sign problem and related phenomena.

Findings

Quantified the severity of the sign problem at high isospin density.

Mapped the low-energy theory to a known random matrix model.

Explained the Silver Blaze phenomenon in this regime.

Abstract

We generalize QCD at asymptotically large isospin chemical potential to an arbitrary even number of flavors. We also allow for small quark chemical potentials, which stress the coincident Fermi surfaces of the paired quarks and lead to a sign problem in Monte Carlo simulations. We derive the corresponding low-energy effective theory in both $p$- and $\epsilon$-expansion and quantify the severity of the sign problem. We construct the random matrix theory describing our physical situation and show that it can be mapped to a known random matrix theory at low baryon density so that new insights can be gained without additional calculations. In particular, we explain the Silver Blaze phenomenon at high isospin density. We also introduce stressed singular values of the Dirac operator and relate them to the pionic condensate. Finally we comment on extensions of our work to two-color QCD.