Renormalization Group Studies of Dense Relativistic Systems

TL;DR

This paper advances the understanding of dense relativistic matter by developing new renormalization group methods and regulator functions to analyze phase transitions and Cooper instabilities, with applications to quark-diquark models.

Contribution

It introduces a new class of regulator functions for functional RG studies tailored to systems with Cooper instabilities and discusses systematic derivative expansion and regularization schemes.

Findings

New regulator functions suitable for Cooper instability analysis

Systematic application of derivative expansion in dense matter

Demonstration with a quark-diquark model

Abstract

Dense relativistic matter has attracted a lot of attention over many decades now, with a focus on an understanding of the phase structure and thermodynamics of dense strong-interaction matter. The analysis of dense strong-interaction matter is complicated by the fact that the system is expected to undergo a transition from a regime governed by spontaneous chiral symmetry breaking at low densities to a regime governed by the presence of a Cooper instability at intermediate and high densities. Renormalization group (RG) approaches have played and still play a prominent role in studies of dense matter in general. In the present work, we study RG flows of dense relativistic systems in the presence of a Cooper instability and analyze the role of the Silver-Blaze property. In particular, we critically assess how to apply the derivative expansion to study dense-matter systems in a systematic fashion. This also involves a detailed discussion of regularization schemes. Guided by these formal developments, we introduce a new class of regulator functions for functional RG studies which is suitable to deal with the presence of a Cooper instability in relativistic theories. We close by demonstrating its application with the aid of a simple quark-diquark model.