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 ε-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.
Highlights
Only theoretically intriguing, the equivalence provides us with a means of extracting low-energy constants in ChPT from lattice QCD data, where Dirac eigenvalues are computable
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
It was found that the sign problem is manifested in an extreme oscillation of the spectral density of the Dirac operator, and that the latter is responsible for the fact that observables in QCD at T = 0 are independent of μq below roughly one third of the nucleon mass, even though the fermion determinant itself depends on μq
Summary
Assuming even Nf , we consider QCD with Nf /2 pairs of u and d quarks. We introduce chemical potentials of the form μu,f = −μI + μu,f for the u quarks and μd,f = μI + μd,f for the d quarks, respectively, where we assume |μi,f | μI for i = u, d and all f. We consider QCD at large isospin chemical potential μI but allow for small quark chemical potentials on top of μI. In this paper we always work in Euclidean space-time unless stated otherwise. Which implies μI = Tr[μd − μu]/Nf. which implies μI = Tr[μd − μu]/Nf Not imposing this condition leads to an ambiguity in the effective theory that is discussed in appendix A, which should best be read after section 3.1.2
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