Color superconductivity on the lattice -- analytic predictions from QCD in a small box

Abstract

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.

30 pages, 15 figures, 1 table, v2: A.3 modified, Ref. [57] added

References in corpus (6)

• Color superconductivity in dense quark matter
• Tensor renormalization group approach to 2D classical lattice models
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Phase transitions in neutron stars and their links to gravitational waves
• Worldvolume approach to the tempered Lefschetz thimble method
• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations

Cited by in corpus (3)

• Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density
• The dynamics of zero modes in lattice gauge theory -- difference between SU(2) and SU(3) in 4D