Functional renormalization group approach to color superconducting phase transition

Gergely Fejős,Naoki Yamamoto

doi:10.1007/jhep12(2019)069

Abstract

We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar SU(Nc) gauge theories by calculating the β function of the gauge coupling in arbitrary dimension d based on two different regularization schemes. We find that in d = 3, due to gluon fluctuation effects, the β function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.

Highlights

The one-loop result of the Coleman-Weinberg potential, become invalid
We investigate the order of the color superconducting phase transition using the functional renormalization group approach
It was only shown recently in an analytic fashion via the functional renormalization group (FRG) framework that, ordinary superconductivity does possess nontrivial charged fixed points [16, 17] describing the possibility of a second-order transition in the system, in agreement with Kleinert’s duality argument [13] and Monte-Carlo simulations [18]; for reviews of FRG, see, e.g. [19,20,21]

Summary

Ginzburg-Landau theory of color superconductivity

We first briefly review the Ginzburg-Landau (GL) theory of color superconductivity [4, 5]. The idea of the GL theory is to expand the thermodynamic potential of a system in terms of an order parameter and its derivatives near the second-order or weak first-order phase transition. In the case of color superconductivity in QCD with Nc = 3 and Nf = 3, the order parameter is the scalar field φγn defined by ψlαCγ5ψmβ ∼ αβγ lmnφγn ,. The formation of the quark-quark pairing is assumed to be in the parity-even, s-wave, and color-flavor antisymmetric channel. The assumption that the pairing takes place in the color antisymmetric channel is justified at sufficiently high density, where the dominant one-gluon exchange interaction at weak coupling is attractive. We will consider generic scalar SU(Nc) gauge theories (which includes the GL theory of color superconductivity with Nc = 3 above) in d-dimensional Euclidean space:.

Basics of the functional renormalization group

Diagrammatics

Gauge wavefunction renormalization

Vertex regulators

Conclusions

A Common integrals