Abstract
The difficulty of describing the gauge dependent bi-quark condensate in the QCD colour superconducting phase has made it hard to construct a holographic dual of the state. To side step this problem, we argue that near the chiral restoration transition in the temperature-chemical potential plane, the strongly coupled gluons are likely completely gapped so that the colour quantum numbers of the quarks can be thought of below that gap as global indices. A standard AdS-superconductor model can then be used to analyze the fermionic gap formation. We investigate the role of four-fermion interactions, which might be used to include the gapped QCD interactions, on the vacuum and metastable vacua of the model. It turns out to be easiest to simply relate the standard interaction of the holographic superconductor to the strength of the gapped gluons. The result is a holographic description of the QCD colour superconducting phase diagram. We take a first look at how quark mass enters and causes a transition between the colour flavour locked phase and the 2SC phase.
Highlights
A fermionic system at finite chemical potential is expected to develop a Fermi surface
The presence of the mass leads to a lower value of the Fermi momentum, which will reduce the condensate, and relative differences in the Fermi surface levels for different quark flavors are expected to frustrate the formation of the color-flavor locked condensate
We have attempted to side step this issue by arguing that at strong coupling and intermediate temperatures and chemical potentials the gluons are likely gapped by the plasma
Summary
A fermionic system at finite chemical potential is expected to develop a Fermi surface. We will conclude we should just choose to tune the intrinsic pairing interaction of the holographic model to represent the broken QCD interactions on the global color degrees of freedom (d.o.f.) The goal of this Paper is to study such broken gauge interactions in the quark gluon plasma to develop a sensible description of the CSC phase in the QCD phase diagram. As the strange quark becomes massive, the condensates of the top two rows (Δ1, Δ2) switch off, and we expect to find a vacuum expectation value (vev) for the triplet, SU(2) flavor singlet of the bottom row (Δ3)—this is the 2SC phase of the massless two flavor case Note all of these states carry net color charge, we have argued the main source of gluon mass is the Debye screening rather than the Meissner induced mass.
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