Study of color superconductivity with Ginzburg-Landau effective action on the lattice

TL;DR

This study uses lattice simulations of the Ginzburg-Landau effective theory to analyze thermal phase transitions in color superconductivity, distinguishing phases and identifying the nature of phase transitions.

Contribution

It provides a gauge-invariant lattice simulation approach to study phase transitions in color superconductivity, including phase distinctions and transition orders.

Findings

First-order transitions due to thermal gluons

Clear distinction between 2SC and CFL phases

Phase structure mapped in coupling-constant space

Abstract

We study thermal phase transitions of color superconductivity by the lattice simulations of the Ginzburg-Landau (GL) effective theory. The theory is equivalent to the SU_ f(3) cross SU_c(3) Higgs model coupled to SU_c(3) color gauge fields. From the eigenvalues of a 3-by-3 gauge-invariant diquark composite, a clear distinction between the 2-flavor color superconductivity (2SC) and the color flavor locking (CFL) phase is made in a gauge invariant manner. The thermal transitions between the normal phase and the superconducting phases are found to be first-order due to thermal gluons. The phase structure in the coupling-constant space is numerically explored and three patterns of phase transition, i.e., normal to 2SC, normal to CFL and normal to CFL via 2SC, are found in the chiral limit. These results agree qualitatively with the weak-coupling analysis of the GL theory.