The Condensed Matter Physics of QCD

TL;DR

The paper formulates high-density QCD in the language of condensed-matter physics, showing that arbitrarily weak attraction near the Fermi surface generically drives diquark pairing and color superconductivity. The CFL phase, with a diquark condensate that locks color and flavor, spontaneously breaks color and chiral symmetries while yielding a massive gluon spectrum and a set of Nambu-Goldstone modes, and it features a rotated electromagnetism that preserves a massless tilde-photon and integer charges. Beyond CFL, the authors analyze 2SC and other flavor/charge configurations, derive gap equations via variational and diagrammatic methods, and obtain asymptotic weak-coupling results for the gap $\Delta$, showing $\Delta \sim \mu \,\exp(-\text{const}/g)$ with a large prefactor. The phase diagram and astrophysical implications are developed, including consequences for neutron-star equation of state, cooling, magnetic-field evolution, r-mode instabilities, and possible crystalline (LOFF) phases and glitches, suggesting observable signatures and guiding future lattice and analytical studies to map high-density QCD.

Abstract

Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS theory make a rigorous analysis possible. New phases of matter with remarkable properties are predicted. They provide a theoretical laboratory within which chiral symmetry breaking and confinement can be studied at weak coupling. They may also play a role in the description of neutron star interiors. We discuss the phase diagram of QCD as a function of temperature and density, and close with a look at possible astrophysical signatures.

Figures (4)

• Figure 1: QCD Phase diagram for two massless quarks. Chiral symmetry is broken in the hadronic phase and is restored elsewhere in the diagram. The chiral phase transition changes from second to first order at a tricritical point. The phase at high density and low temperature is a color superconductor in which up and down quarks with two out of three colors pair and form a condensate. The transition between this 2SC phase and the QGP phase is likely first order. The transition on the horizontal axis between the hadronic and 2SC phases is first order. The transition between a nuclear matter "liquid" and a gas of individual nucleons is also marked. At $T=0$, it separates the vacuum phase from the nuclear matter phase; Lorentz-boost symmetry is broken to its right but unbroken to its left. At nonzero temperature, Lorentz-boost symmetry is broken in both the nuclear gas and nuclear liquid, and this line of phase transitions may therefore end. It is thought to end at a critical point at a temperature of order 10 MeV, characteristic of the forces which bind nucleons into nuclei.
• Figure 2: QCD phase diagram for two light quarks. Qualitatively as in Figure 1, except that the introduction of light quark masses turns the second order phase transition into a smooth crossover. The tricritical point becomes the critical endpoint $E$, which can be found in heavy ion collision experiments.
• Figure 3: QCD phase diagram for two light quarks and a strange quark with a mass comparable to that in nature. The presence of the strange quark shifts $E$ to the left, as can be seen by comparing with Figure 2. At sufficiently high density, cold quark matter is necessarily in the CFL phase in which quarks of all three colors and all three flavors form Cooper pairs. The diquark condensate in the CFL phase breaks chiral symmetry, and this phase has the same symmetries as baryonic matter which is dense enough that the nucleon and hyperon densities are comparable. The unlocking phase transition between the CFL and 2SC phases is first order.
• Figure 4: QCD phase diagram for three quarks which are degenerate in mass and which are either massless or light. The CFL phase and the baryonic phase have the same symmetries and may be continuously connected. The dashed line denotes the critical temperature at which baryon-baryon (or quark-quark) pairing vanishes; the region below the dashed line is superfluid. Chiral symmetry is broken everywhere below the solid line, which is a first order phase transition. The question mark serves to remind us that although no transition is required in this region, transition(s) may nevertheless arise as the magnitude of the gap increases qualitatively in going from the hypernuclear to the CFL phase. For quark masses as in nature, the high density region of the map may be as shown in Figure 3 or may be closer to that shown here, albeit with transition(s) in the vicinity of the question mark associated with the onset of nonzero hyperon density and the breaking of $U(1)_S$.ABR2+1