Color superconductivity

Color superconductivity is a phenomenon predicted to occur in quark matter if the baryon density is sufficiently high (well above nuclear density) and the temperature is not too high (well below 10¹² kelvins). Color superconducting phases are to be contrasted with the normal phase of quark matter, which is just a weakly-interacting Fermi liquid of quarks.

In theoretical terms, a color superconducting phase is a state in which the quarks near the Fermi surface become correlated in Cooper pairs, which condense. In phenomenological terms, a color superconducting phase breaks some of the symmetries of the underlying theory, and has a very different spectrum of excitations and very different transport properties from the normal phase.

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Description

Analogy with superconducting metals

It is well known that at low temperature many metals become superconductors. A metal can be viewed as a Fermi liquid of electrons, and below a critical temperature, an attractive phonon-mediated interaction between the electrons near the Fermi surface causes them to pair up and form a condensate of Cooper pairs, which via the Anderson-Higgs mechanism makes the photon massive, leading to the characteristic behaviors of a superconductor; infinite conductivity and the exclusion of magnetic fields (Meissner effect). The crucial ingredients for this to occur are:

1. a liquid of charged fermions
2. an attractive interaction between the fermions
3. low temperature (below the critical temperature)

These ingredients are also present in sufficiently dense quark matter, leading physicists to expect that something similar will happen in that context:

1. quarks carry both electric charge and color charge;
2. the strong interaction between two quarks is powerfully attractive;
3. the critical temperature is expected to be given by the QCD scale, which is of order 100 MeV, or 10¹² kelvins, the temperature of the universe a few minutes after the big bang, so quark matter that we may currently observe in compact stars or other natural settings will be below this temperature.

The fact that a Cooper pair of quarks carries a net color charge, as well as a net electric charge, means that the gluons (which mediate the strong interaction just as photons mediate electromagnetism) become massive in a phase with a condensate of quark Cooper pairs, so such a phase is called a "color superconductor". Actually, in many color superconducting phases the photon itself does not become massive, but mixes with one of the gluons to yield a new massless "rotated photon". This is an MeV-scale echo of the mixing of the hypercharge and W₃ bosons that originally yielded the photon at the TeV scale of electroweak symmetry breaking.

Diversity of color superconducting phases

Unlike an electrical superconductor, color-superconducting quark matter comes in many varieties, each of which is a separate phase of matter. This is because quarks, unlike electrons, come in many species. There are three different colors (red, green, blue) and in the core of a compact star we expect three different flavors (up, down, strange), making nine species in all. Thus in forming the Cooper pairs there is a 9x9 color-flavor matrix of possible pairing patterns. The differences between these patterns are very physically significant: different patterns break different symmetries of the underlying theory, leading to different excitation spectra and different transport properties.

It is very hard to predict which pairing patterns will be favored in nature. In principle this question could be decided by a QCD calculation, since QCD is the theory that fully describes the strong interaction. In the limit of infinite density, where the strong interaction becomes weak because of asymptotic freedom, controlled calculations can be performed, and it is known that the favored phase in three-flavor quark matter is the color-flavor-locked phase. But at the densities that exist in nature these calculations are unreliable, and the only known alternative is the brute-force computational approach of lattice QCD, which unfortunately has a technical difficulty (the "sign problem") that renders it useless for calculations at high quark density and low temperature.

Physicists are currently following the following lines of research on color superconductivity:

1. Performing calculations in the infinite density limit, to get some idea of the behavior at one edge of the phase diagram.
2. Performing calculations of the phase structure down to medium density using a highly simplified model of QCD, the Nambu-Jona-Lasinio (NJL) model, which is not a controlled approximation, but is expected to yield semi-quantitative insights.
3. Writing down an effective theory for the excitations of a given phase, and using it to calculate the physical properties of that phase.
4. Performing astrophysical calculations, using NJL models or effective theories, to see if there are observable signatures by which one could confirm or rule out the presence of specific color superconducting phases in nature (i.e. in compact stars: see next section).

Occurrence in nature

The only known place in the universe where the baryon density might possibly be high enough to produce quark matter, and the temperature is low enough for color superconductivity to occur, is the core of a compact star (often called a "neutron star", a term which prejudges the question of its actual makeup). There are many open questions here:

1. We do not know the critical density at which there would be a phase transition from nuclear matter to some form of quark matter, so we do not know whether compact stars have quark matter cores or not.
2. On the other extreme, it is conceivable that nuclear matter in bulk is actually metastable, and decays into quark matter (the "stable strange matter hypothesis"). In this case, compact stars would consist completely of quark matter all the way to their surface.
3. Assuming that compact stars do contain quark matter, we do not know whether that quark matter is in a color superconducting phase or not. At infinite density one expects color superconductivity, and the attractive nature of the dominant strong quark-quark interaction leads one to expect that it will survive down to lower densities, but there may be a transition to some strongly-coupled phase (e.g. a Bose-Einstein condensate of spatially-bound diquarks).

History

The first physicists to realize that Cooper pairing could occur in quark matter were D. D. Ivanenko and D. F. Kurdgelaidze of Moscow State University ^[1], in 1969. However, their insight was not pursued until the development of QCD as the theory of the strong interaction in the early 1970s. In 1977 Stephen Frautschi, a professor at Caltech, and his graduate student Bertrand Barrois realized that QCD predicts Cooper pairing in high density quark matter, and coined the term "color superconductivity". Barrois was able to get part of his work published in the journal Nuclear Physics ^[2], but that journal rejected the longer manuscript based on his thesis, which impressively anticipated later results such as the exp(-1/g) dependence of the quark condensate on the QCD coupling g. Barrois then left academic physics. At around the same time the subject was also treated by David Bailin and Alexander Love at Sussex University, who studied various pairing patterns in detail, but did not give much attention to the phenomenology of color superconductivity in real-world quark matter ^[3].

Apart from papers by Masaharu Iwaskai and T. Iwado of Kochi University in 1995 ^[4], there was little activity until 1998, when there was a major upsurge of interest in dense quark matter and color superconductivity, sparked by the simultaneously published work of two groups, one at the Institute for Advanced Study in Princeton ^[5] and the other at SUNY Stonybrook ^[6]. These physicists pointed out that the strength of the strong interaction makes the phenomenon much more significant than had previously been suggested. These and other groups went on to investigate the complexity of the many possible phases of color superconducting quark matter, and perform accurate calculations in the well-controlled limit of infinite density. Since then, interest in the topic has steadily grown, with current research (as of 2007) focussing on the detailed mapping of a plausible phase diagram for dense quark matter, and the search for observable signatures of the occurrence of these forms of matter in compact stars.

See also

• Quark matter
• Fermion condensate

Further reading

Popular articles:

• S. Hands, "The phase diagram of QCD", Contemp. Phys. 42, 209 (2001)
• J. Cheyne, G. Cowan, M. Alford, "Superconducting quarks", PPARC Frontiers 21, 16 (2004)

Technical reviews:

• M. Alford, K. Rajagopal, T. Schäfer, A. Schmitt, "Color superconductivity in dense quark matter", Reviews of Modern Physics, to be published
• K. Rajagopal and F. Wilczek, "The condensed matter physics of QCD", arXiv.org:hep-ph/0011333
• M. Alford, "Color superconducting quark matter", Ann. Rev. Nucl. Part. Sci. 51, 131 (2001)
• G. Nardulli, "Effective description of QCD at very high densities", Riv. Nuovo Cim. 25N3, 1 (2002)
• T. Schäfer, "Quark matter", arxiv.org:hep-ph/0304281
• D. Rischke, "The quark-gluon plasma in equilibrium", Prog. Part. Nucl. Phys. 52, 197 (2004)
• S. Reddy, "Novel phases at high density and their roles in the structure and evolution of neutron stars", Acta Phys. Polon. B 33, 4101 (2002)
• I. Shovkovy, Two lectures on color superconductivity, Found.Phys. 35 (2005) 1309-1358, online version

References

1. ^ D. D. Ivanenko and D. F. Kurdgelaidze, Lett. Nuovo Cim. IIS1, 13-16 (1969)
2. ^ B. Barrois, Nucl. Phys. B129, 390 (1977)
3. ^ D. Bailin and A. Love, Phys. Rept. 107, 325 (1984)
4. ^ M. Iwasaki and T. Iwado, Phys. Lett. B350, 163 (1995)
5. ^ M. Alford, K. Rajagopal and F. Wilczek, Phys. Lett. B422, 247 (1998)
6. ^ R. Rapp, T. Schafer, E. Shuryak and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998)