The first lecture provides an introduction to the physics of color superconductivity in cold dense quark matter. The main color superconducting phases are briefly described and their properties are listed. The second lecture covers recent developments in studies of color superconducting phases in neutral and β-equilibrated matter. The properties of gapless color superconducting phases are discussed.
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References
K. Hagiwara et al. (2002) Phys. Rev. D. 66 010001 Occurrence Handle10.1103/PhysRevD.66.010001 Occurrence Handle2002PhRvD..66a0001H
D. Ivanenko and D. F. Kurdgelaidze , Astrofiz. 1, 479 (1965); Lett. Nuovo Cim. 2, 13 (1969); N. Itoh, Prog. Theor. Phys. 44, 291 (1970); F. Iachello, W. D. Langer and A. Lande, Nucl. Phys. A 219, 612 (1974).
H. D. Politzer , Phys. Rev. Lett. 30, 1346 (1973); D. J. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973); Phys. Rev. D 9, 980 (1974).
J. C. Collins M. J. Perry (1975) Phys. Rev. Lett. 34 1353 Occurrence Handle10.1103/PhysRevLett.34.1353 Occurrence Handle1975PhRvL..34.1353C
J. I. Kapusta (1989) Finite-temperature Field Theory University Press Cambridge
A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974); A. Chodos, R. L. Jaffe, K. Johnson and C. B. Thorn, Phys. Rev. D 10, 2599 (1974).
B. A. Freedman L. D. McLerran (1977) Phys Rev D. 16 1169 Occurrence Handle1977PhRvD..16.1169F
L. N. Cooper (1956) Phys. Rev. 104 1189 Occurrence Handle10.1103/PhysRev.104.1189 Occurrence Handle1956PhRv..104.1189C Occurrence Handle0074.23705
J. Bardeen , L. N. Cooper and J. R. Schrieffer , Phys. Rev. 106, 162 (1957); Phys. Rev. 108, 1175 (1957).
K. Rajagopal and F. Wilczek, hep-ph/0011333; D. K. Hong, Acta Phys. Polon. B 32, 1253 (2001); M. Alford, Ann. Rev. Nucl. Part. Sci. 51, 131 (2001); T. Schäfer, hep-ph/0304281; D. H. Rischke, Prog. Part. Nucl. Phys. 52, 197 (2004); H.-c. Ren, hep-ph/0404074; M. Huang, hep-ph/0409167.
B. C. Barrois, Nucl. Phys. B 129, 390 (1977); S. C. Frautschi, in Hadronic Matter at Extreme Energy Density, N. Cabibbo and L. Sertorio eds. (Plenum Press, 1980).
D. Bailin and A. Love, Nucl. Phys. B 190, 175 (1981); Nucl. Phys. B 205, 119 (1982); Phys. Rep. 107, 325 (1984).
M. Alford, K. Rajagopal and F. Wilczek, Phys. Lett. B 422, 247 (1998); R. Rapp, T. Schäfer, E. V. Shuryak and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998).
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961); Phys. Rev. 124, 246 (1961).
G. W. Carter and D. Diakonov, Phys. Rev. D 60, 016004 (1999); J. Berges and K. Rajagopal, Nucl. Phys. B 538, 215 (1999); M. Buballa and M. Oertel, Nucl. Phys. A 703, 770 (2002); F. Gastineau, R. Nebauer and J. Aichelin, Phys. Rev. C 65, 045204 (2002); M. Huang, P. F. Zhuang and W. Q. Chao, Phys. Rev. D 65, 076012 (2002).
M. Buballa (2005) Phys. Rept. 407 205 Occurrence Handle10.1016/j.physrep.2004.11.004 Occurrence Handle2005PhR...407..205B
M. Huang P. F. Zhuang W. Q. Chao (2003) Phys. Rev. D. 67 065015 Occurrence Handle10.1103/PhysRevD.67.065015 Occurrence Handle2003PhRvD..67f5015H
T.M. Schwarz S.P. Klevansky G. Papp (1999) Phys. Rev. C. 60 055205 Occurrence Handle10.1103/PhysRevC.60.055205 Occurrence Handle1999PhRvC..60e5205S
D. J. Gross, R. D. Pisarski and L. G. Yaffe, Rev. Mod. Phys. 53, 43 (1981); E. V. Shuryak, Nucl. Phys. B 203, 140 (1982); D. T. Son, M. A. Stephanov and A. R. Zhitnitsky, Phys. Lett. B 510, 167 (2001).
R. Casalbuoni Z.Y. Duan F. Sannino (2000) Phys. Rev. D. 62 094004 Occurrence Handle10.1103/PhysRevD.62.094004 Occurrence Handle2000PhRvD..62i4004C
V. A. Miransky, I. A. Shovkovy and L. C. R. Wijewardhana, Phys. Rev. D 62, 085025 (2000); Phys. Rev. D 64, 096002 (2001).
D. H. Rischke D. T. Son M. A. Stephanov (2001) Phys. Rev. Lett. 87 062001 Occurrence Handle10.1103/PhysRevLett.87.062001 Occurrence Handle2001PhRvL..87f2001R
W. E. Brown, J. T. Liu and H.-c. Ren, Phys. Rev. D 61, 114012 (2000); Q. Wang and D. H. Rischke, Phys. Rev. D 65, 054005 (2002).
H. Vija M. H. Thoma (1995) Phys. Lett. B. 342 212 Occurrence Handle1995PhLB..342..212V
C. Manuel (1996) Phys. Rev. D. 53 5866 Occurrence Handle10.1103/PhysRevD.53.5866 Occurrence Handle1996PhRvD..53.5866M
V. A. Miransky, G. W. Semenoff, I. A. Shovkovy and L. C. R. Wijewardhana, Phys. Rev. D 64, 025005 (2001); P. Jaikumar and I. Zahed, Phys. Rev. D 64, 014035 (2001).
U.W. Heinz (1986) Annals. Phys. 168 148 Occurrence Handle10.1016/0003-4916(86)90114-4
D.T. Son (1999) Phys. Rev. D. 59 094019 Occurrence Handle1999PhRvD..59i4019S Occurrence Handle1680596
Hong D.K., Miransky V. A., Shovkovy I. A, Wijewardhana L. C. R. Phys. Rev. D 61, 056001 (2000); T. Schäfer and F. Wilczek, Phys. Rev. D 60, 114033 (1999); S. D. H. Hsu and M. Schwetz, Nucl. Phys. B 572, 211 (2000).
Pisarski R.D, Rischke D.H, Phys. Rev. D 61, 051501 (2000); Phys. Rev. D 61, 074017 (2000).
N. Iwamoto (1980) Phys. Rev. Lett. 44 1637 Occurrence Handle10.1103/PhysRevLett.44.1637 Occurrence Handle1980PhRvL..44.1637I
The pressure correction due to color superconductivity is determined, up to a sign, by the value of the effective potential at its minimum in V. A. Miransky, I. A. Shovkovy and L. C. R. Wijewardhana, Phys. Lett. B 468, 270 (1999).
I. A. Shovkovy and P. J. Ellis, Phys. Rev. C 66, 015802 (2002); C. Manuel, A. Dobado and F. J. Llanes-Estrada, hep-ph/0406058.
G. Lugones J.E. Horvath (2002) Phys. Rev. D. 66 074017 Occurrence Handle10.1103/PhysRevD.66.074017 Occurrence Handle2002PhRvD..66g4017L
M. Alford S. Reddy (2003) Phys. Rev. D. 67 074024 Occurrence Handle2003PhRvD..67g4024A
R. C. Tolman, Phys. Rev. 55, 364 (1939); J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 (1939).
S. Banik D. Bandyopadhyay (2003) Phys. Rev. D. 67 123003 Occurrence Handle10.1103/PhysRevD.67.123003 Occurrence Handle2003PhRvD..67l3003B
M Baldo M. Buballa F. Burgio F. Neumann M Oertel H. J. Schulze (2003) Phys. Lett. B. 562 153 Occurrence Handle2003PhLB..562..153B
I. Shovkovy M. Hanauske M. Huang (2003) Phys. Rev. D. 67 103004 Occurrence Handle10.1103/PhysRevD.67.103004 Occurrence Handle2003PhRvD..67j3004S
D. Blaschke H. Grigorian D.N. Aguilera S. Yasui H. Toki (2003) AIP. Conf. Proc. 660 209 Occurrence Handle2003AIPC..660..209B
M. Buballa F. Neumann M. Oertel I. Shovkovy (2004) Phys. Lett. B. 595 36 Occurrence Handle2004PhLB..595...36B
A. R. Bodmer, Phys. Rev. D 4, 1601 (1971); E. Witten, Phys. Rev. D 30, 272 (1984); C. Alcock, E. Farhi and A. Olinto, Astrophys. J. 310, 261 (1986).
M. G. Alford K. Rajagopal F. Wilczek (1999) Nucl. Phys. B. 537 443 Occurrence Handle10.1016/S0550-3213(98)00668-3 Occurrence Handle1999NuPhB.537..443A
I. A. Shovkovy and L. C. R. Wijewardhana, Phys. Lett. B 470, 189 (1999); T. Schäfer, Nucl. Phys. B 575, 269 (2000).
T. Schäfer (2003) Nucl. Phys. A. 728 251 Occurrence Handle2003NuPhA.728..251S Occurrence Handle1058.81758
P.W. Anderson N. Itoh (1975) Nature. 256 25 Occurrence Handle10.1038/256025a0 Occurrence Handle1975Natur.256...25A
I.A Shovkovy P.J. Ellis (2003) Phys. Rev. C. 67 048801 Occurrence Handle10.1103/PhysRevC.67.048801 Occurrence Handle2003PhRvC..67d8801S
C. Vogt R. Rapp R. Ouyed (2004) Nucl. Phys. A. 735 543 Occurrence Handle2004NuPhA.735..543V
J. Gasser and H. Leutwyler, Nucl. Phys. B 250, 465 (1985); Ann. Phys. 158, 142 (1984); G. Ecker, Prog. Part. Nucl. Phys. 35, 1 (1995); A. Pich, Rept. Prog. Phys. 58, 563 (1995).
D.K. Hong M. Rho I. Zahed (1999) Phys. Lett. B. 468 261 Occurrence Handle1999PhLB..468..261H
R Casalbuoni R. Gatto (1999) Phys. Lett. B. 464 111 Occurrence Handle1999PhLB..464..111C
D. T. Son and M. A. Stephanov, Phys. Rev. D 61, 074012 (2000); Erratum: Phys. Rev. D 62, 059902 (2000).
K. Zarembo, Phys. Rev. D 62, 054003 (2000); S. R. Beane, P. F. Bedaque and M. J. Savage, Phys. Lett. B 483, 131 (2000); V. A. Miransky, I. A. Shovkovy and L. C. R. Wijewardhana, Phys. Rev. D 63, 056005 (2001).
D. T. Son M. A Stephanov A. R. Zhitnitsky (2001) Phys. Rev. Lett. 86 3955 Occurrence Handle2001PhRvL..86.3955S
C. Manuel and M. H. G. Tytgat, Phys. Lett. B 479, 190 (2000); T. Schäfer, Phys. Rev. D 65, 074006 (2002).
D. K. Hong, Phys. Lett. B 473, 118 (2000); Nucl. Phys. B 582, 451 (2000); G. Nardulli, Riv. Nuovo Cim. 25N3, 1 (2002); P. T. Reuter, Q. Wang and D. H. Rischke, Phys. Rev. D 70, 114029 (2004).
P. F. Bedaque T. Schäfer (2002) Nucl. Phys. A. 697 802 Occurrence Handle2002NuPhA.697..802B
D.B. Kaplan S. Reddy (2002) Phys. Rev. D. 65 054042 Occurrence Handle10.1103/PhysRevD.65.054042 Occurrence Handle2002PhRvD..65e4042K
A. Kryjevski D. B. Kaplan T. Schäfer (2005) Phys. Rev. D. 71 034004 Occurrence Handle2005PhRvD..71c4004K
V. A. Miransky and I. A. Shovkovy, Phys. Rev. Lett. 88, 111601 (2002); T. Schäfer, D. T. Son, M. A. Stephanov, D. Toublan and J. J. M. Verbaarschot, Phys. Lett. B 522, 67 (2001).
M. Iwasaki T. Iwado (1995) Phys. Lett. B. 350 163 Occurrence Handle1995PhLB..350..163I
T. Schäfer, Phys. Rev. D 62, 094007 (2000); M. G. Alford, J. A. Bowers, J. M. Cheyne and G. A. Cowan, Phys. Rev. D 67, 054018 (2003); M. Buballa, J. Hošek and M. Oertel, Phys. Rev. Lett. 90, 182002 (2003).
A. Schmitt, Q. Wang and D. H. Rischke, Phys. Rev. Lett. 91, 242301 (2003); Phys. Rev. D 69, 094017 (2004).
A. Schmitt (2005) Phys. Rev. D. 71 054016 Occurrence Handle10.1103/PhysRevD.71.054016 Occurrence Handle2005PhRvD..71e4016S
A. Schmitt I. A. Shovkovy Q. Wang (2005) Phys. Rev. Lett 94 211101 Occurrence Handle10.1103/PhysRevLett.94.211101 Occurrence Handle2005PhRvL..94u1101S
D. Blaschke, D. N. Voskresensky and H. Grigorian, astro-ph/0403171.
T. Schäfer and F. Wilczek, Phys. Rev. Lett. 82, 3956 (1999); Phys. Rev. D 60, 074014 (1999).
M. Alford K. Rajagopal (2002) JHEP 0206 031 Occurrence Handle2002JHEP...06..031A
A.W. Steiner S. Reddy M. Prakash (2002) Phys. Rev. D 66 094007 Occurrence Handle10.1103/PhysRevD.66.094007 Occurrence Handle2002PhRvD..66i4007S
I. Shovkovy M. Huang (2003) Phys. Lett. B 564 205 Occurrence Handle2003PhLB..564..205S
E. Gubankova W.V. Liu F. Wilczek (2003) Phys. Rev. Lett 91 032001 Occurrence Handle10.1103/PhysRevLett.91.032001 Occurrence Handle2003PhRvL..91c2001G
A. Mishra H. Mishra (2004) Phys. Rev. D 69 014014 Occurrence Handle10.1103/PhysRevD.69.014014 Occurrence Handle2004PhRvD..69a4014M
S. B. Rüster D. H. Rischke (2004) Phys. Rev. D 69 045011 Occurrence Handle2004PhRvD..69d5011R
M. Huang I. Shovkovy (2003) Nucl. Phys. A 729 835 Occurrence Handle2003NuPhA.729..835H
J.F. Liao P.F. Zhuang (2003) Phys. Rev. D 68 114016 Occurrence Handle10.1103/PhysRevD.68.114016 Occurrence Handle2003PhRvD..68k4016L
M. Alford C. Kouvaris K. Rajagopal (2004) Phys. Rev. Lett 92 222001 Occurrence Handle10.1103/PhysRevLett.92.222001 Occurrence Handle2004PhRvL..92v2001A
M. Alford C. Kouvaris K. Rajagopal (2005) Phys. Rev. D 71 054009 Occurrence Handle2005PhRvD..71e4009A
K. Iida T. Matsuura M. Tachibana T. Hatsuda (2004) Phys. Rev. Lett 93 132001 Occurrence Handle10.1103/PhysRevLett.93.132001 Occurrence Handle2004PhRvL..93m2001I
S. B. Rüster, I. A. Shovkovy and D. H. Rischke, Nucl. Phys. A 743, 127 (2004); I. A. Shovkovy, S. B. Rüster and D. H. Rischke, J. Phys. G 31, S849 (2005).
K. Fukushima C. Kouvaris K. Rajagopal (2005) Phys. Rev. D 71 034002 Occurrence Handle2005PhRvD..71c4002F
S. B. Rüster, V. Werth, M. Buballa, I. A. Shovkovy and D. H. Rischke, hep-ph/0503184; D. Blaschke, S. Fredriksson, H. Grigorian, A.M. Öztaş and F. Sandin, hep-ph/0503194.
S. Reddy G. Rupak (2005) Phys. Rev. C 71 025201 Occurrence Handle10.1103/PhysRevC.71.025201 Occurrence Handle2005PhRvC..71b5201R
W.V. Liu F. Wilczek (2003) Phys. Rev. Lett 90 047002 Occurrence Handle2003PhRvL..90d7002L
B. Deb A. Mishra H. Mishra P.K. Panigrahi (2004) Phys. Rev. A 70 011604(R) Occurrence Handle10.1103/PhysRevA.70.011604 Occurrence Handle2004PhRvA..70a1604D
W. V. Liu F. Wilczek P. Zoller (2004) Phys. Rev. A 70 033603 Occurrence Handle2004PhRvA..70c3603L
M. M. Forbes E. Gubankova W. V. Liu F. Wilczek (2005) Phys. Rev. Lett 94 017001 Occurrence Handle2005PhRvL..94a7001F
E. Gubankova F. Wilczek E. G. Mishchenko (2005) Phys. Rev. Lett 94 110402 Occurrence Handle10.1103/PhysRevLett.94.110402 Occurrence Handle2005PhRvL..94k0402G
F. Neumann M. Buballa M. Oertel (2003) Nucl. Phys. A 714 481 Occurrence Handle2003NuPhA.714..481N
P. F. Bedaque, H. Caldas and G. Rupak, Phys. Rev. Lett. 91, 247002 (2003); H. Caldas, Phys. Rev. A 69, 063602 (2004).
A. Gerhold and A. Rebhan, Phys. Rev. D 68, 011502 (2003); A. Kryjevski, Phys. Rev. D 68, 074008 (2003); D. D. Dietrich and D. H. Rischke, Prog. Part. Nucl. Phys. 53, 305 (2004).
R. L. Stratonovich, Doklady Akad. Nauk S.S.S.R. 115, 1097 (1957); [translation: Sov. Phys. Doklady 2, 416 (1958)]; J. Hubbard, Phys. Rev. Lett. 3, 77 (1959).
M. Huang and I. A. Shovkovy, Phys. Rev. D 70, 051501(R) (2004); Phys. Rev. D 70, 094030 (2004).
D. H. Rischke, Phys. Rev. D 62, 034007 (2000); D. H. Rischke and I. A. Shovkovy, Phys. Rev. D 66, 054019 (2002).
H. Müther A. Sedrakian (2003) Phys. Rev. D 67 085024 Occurrence Handle2003PhRvD..67h5024M
A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965); P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964).
M. G. Alford, J. A. Bowers and K. Rajagopal, Phys. Rev. D 63, 074016 (2001); J. A. Bowers, J. Kundu, K. Rajagopal and E. Shuster, Phys. Rev. D 64, 014024 (2001); R. Casalbuoni, R. Gatto, M. Mannarelli and G. Nardulli, Phys. Rev. D 66, 014006 (2002); I. Giannakis, J. T. Liu, and H.-c. Ren, Phys. Rev. D 66, 031501 (2002); J. A. Bowers and K. Rajagopal, Phys. Rev. D 66, 065002 (2002).
K. Rajagopal F. Wilczek (2001) Phys. Rev. Lett 86 3492 Occurrence Handle10.1103/PhysRevLett.86.3492 Occurrence Handle2001PhRvL..86.3492R
N. K. Glendenning (1992) Phys. Rev. D 46 1274 Occurrence Handle1992PhRvD..46.1274G
F. Weber (1999) Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics Institute of Physics Bristol
H. Heiselberg, C. J. Pethick and E. F. Staubo, Phys. Rev. Lett. 70, 1355 (1993); N. K. Glendenning and S. Pei, Phys. Rev. C 52, 2250 (1995); N. K. Glendenning and J. Schaffner-Bielich, Phys. Rev. Lett. 81, 4564 (1998).
T. Norsen and S. Reddy, Phys. Rev. C 63, 065804 (2001); D. N. Voskresensky, M. Yasuhira and T. Tatsumi, Nucl. Phys. A 723, 291 (2003).
P. Slane D. J. Helfand S. S. Murray (2002) Astrophys. J 571 L45 Occurrence Handle10.1086/341179 Occurrence Handle2002ApJ...571L..45S
J. J. Drake et al. (2002) Astrophys. J 572 996 Occurrence Handle10.1086/340368 Occurrence Handle2002ApJ...572..996D
D. G. Yakovlev A. D. Kaminker P. Haensel O. Y. Gnedin (2002) Astron. & Astrophys 389 L24 Occurrence Handle2002A&A...389L..24Y
F. M. Walter J. M. Lattimer (2002) Astrophys. J 576 L145 Occurrence Handle10.1086/343850 Occurrence Handle2002ApJ...576L.145W
D. K. Hong S. D. H. Hsu (2003) Phys. Rev. D 68 034011 Occurrence Handle2003PhRvD..68c4011H
S. Hands, I. Montvay, S. Morrison, M. Oevers, L. Scorzato, and J. Skullerud, Eur. Phys. J. C 17, 285 (2000); J. B. Kogut, D. K. Sinclair, S. J. Hands and S. E. Morrison, Phys. Rev. D 64, 094505 (2001).
K. G. Wilson, Phys. Rev. D 10, 2445 (1974); M. Creutz, Phys. Rev. D 21, 2308 (1980).
F. Karsch, E. Laermann and A. Peikert, Nucl. Phys. B 605, 579 (2001); M. Asakawa, T. Hatsuda and Y. Nakahara, Prog. Part. Nucl. Phys. 46, 459 (2001); F. Csikor, Z. Fodor, S. D. Katz and T. G. Kovacs, JHEP 0311, 070 (2003).
F. Karsch, Nucl. Phys. Proc. Suppl. 83, 14 (2000); Z. Fodor and S. D. Katz, Phys. Lett. B 534, 87 (2002); JHEP 0203, 014 (2002); C. R. Allton et al., Phys. Rev. D 66, 074507 (2002).
M. A. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov and J. J. M. Verbaarschot, Phys. Rev. D 58, 096007 (1998); M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev. Lett. 81, 4816 (1998); P. de Forcrand and O. Philipsen, Nucl. Phys. B 642, 290 (2002).
K. Rajagopal (1999) Nucl. Phys. A 661 150 Occurrence Handle1999NuPhA.661..150R Occurrence Handle0995.81516
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*Lectures delivered at the IARD 2004 conference, Saas Fee, Switzerland, June 12–19, 2004, and at the Helmholtz International Summer School and Workshop on Hot points in Astrophysics and Cosmology, JINR, Dubna, Russia, August 2 – 13, 2004.
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Shovkovy, I.A. Two Lectures on Color Superconductivity*. Found Phys 35, 1309–1358 (2005). https://doi.org/10.1007/s10701-005-6440-x
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DOI: https://doi.org/10.1007/s10701-005-6440-x