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

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.

arXiv comment32 pages, 4 figures. v2: title change and text improvements, the version to appear in JHEP

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• Dropping the independence: singular values for products of two coupled random matrices
• Perturbative thermodynamics at nonzero isospin density for cold QCD
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Heavy-tailed chiral random matrix theory
• Chiral random matrix theory for single-flavor spin-one Cooper pairing
• Phonon modes of magnetic vortex lattices in finite isospin chiral perturbation theory
• Analysis of the QCD Kondo phase using random matrices
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• Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
• Chiral random matrix theory for colorful quark-antiquark condensates