Abstract
We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar SU(Nc) gauge theories by calculating the β function of the gauge coupling in arbitrary dimension d based on two different regularization schemes. We find that in d = 3, due to gluon fluctuation effects, the β function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.
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M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys.B 537 (1999) 443 [hep-ph/9804403] [INSPIRE].
D. Bailin and A. Love, Superfluidity and superconductivity in relativistic fermion systems, Phys. Rept.107 (1984) 325 [INSPIRE].
M.G. Alford, A. Schmitt, K. Rajagopal and T. Schäfer, Color superconductivity in dense quark matter, Rev. Mod. Phys.80 (2008) 1455 [arXiv:0709.4635] [INSPIRE].
K. Iida and G. Baym, The superfluid phases of quark matter: Ginzburg-Landau theory and color neutrality, Phys. Rev.D 63 (2001) 074018 [Erratum ibid.D 66 (2002) 059903] [hep-ph/0011229] [INSPIRE].
K. Iida and G. Baym, Superfluid phases of quark matter. 3. Supercurrents and vortices, Phys. Rev.D 66 (2002) 014015 [hep-ph/0204124] [INSPIRE].
R.D. Pisarski and D.H. Rischke, A first order transition to and then parity violation in, a color superconductor, Phys. Rev. Lett.83 (1999) 37 [nucl-th/9811104] [INSPIRE].
T. Matsuura, K. Iida, T. Hatsuda and G. Baym, Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity, Phys. Rev.D 69 (2004) 074012 [hep-ph/0312042] [INSPIRE].
I. Giannakis, D.-f. Hou, H.-c. Ren and D.H. Rischke, Gauge field fluctuations and first-order phase transition in color superconductivity, Phys. Rev. Lett.93 (2004) 232301 [hep-ph/0406031] [INSPIRE].
J.L. Noronha et al., Absence of the London limit for the first-order phase transition to a color superconductor, Phys. Rev.D 73 (2006) 094009 [hep-ph/0602218] [INSPIRE].
A. Das, Phase transition in SU(N ) × U(1) gauge theory with many fundamental bosons, Phys. Rev.B 97 (2018) 214429 [arXiv:1802.08555] [INSPIRE].
R.D. Pisarski, Critical line for H superfluidity in strange quark matter?, Phys. Rev.C 62 (2000) 035202 [nucl-th/9912070] [INSPIRE].
B.i. Halperin, T.C. Lubensky and S.K. Ma, First order phase transitions in superconductors and smectic A liquid crystals, Phys. Rev. Lett.32 (1974) 292 [INSPIRE].
H. Kleinert, Disorder version of the abelian Higgs model and the order of the superconductive phase transition, Lett. Nuovo Cim.35 (1982) 405 [INSPIRE].
H. Kleinert, Vortex origin of tricritical point in Ginzburg-Landau theory, Europhys. Lett.74 (2006) 889.
R. Folk and Y. Holovatch, On the critical fluctuations in superconductors, J. Phys.A 29 (1996) 3409.
G. Fejos and T. Hatsuda, Fixed point structure of the Abelian Higgs model, Phys. Rev.D 93 (2016) 121701 [arXiv:1604.05849] [INSPIRE].
G. Fejos and T. Hatsuda, Renormalization group flows of the N-component Abelian Higgs model, Phys. Rev.D 96 (2017) 056018 [arXiv:1705.07333] [INSPIRE].
S. Mo, J. Hove and A. Sudbo, The order of the metal to superconductor transition, Phys. Rev.B 65 (2002) 104501 [cond-mat/0109260] [INSPIRE].
J. Berges, N. Tetradis and C. Wetterich, Nonperturbative renormalization flow in quantum field theory and statistical physics, Phys. Rept.363 (2002) 223 [hep-ph/0005122] [INSPIRE].
P. Kopietz, L. Bartosch and F. Schütz, Introduction to the functional renormalization group, Springer, Berlin Germany (2010).
B. Delamotte, An introduction to the nonperturbative renormalization group, Lect. Notes Phys.852 (2012) 49 [cond-mat/0702365] [INSPIRE].
M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys.B 417 (1994) 181 [INSPIRE].
M. Reuter and C. Wetterich, Exact evolution equation for scalar electrodynamics, Nucl. Phys.B 427 (1994) 291 [INSPIRE].
B. Bergerhoff, F. Freire, D. Litim, S. Lola and C. Wetterich, Phase diagram of superconductors, Phys. Rev.B 53 (1996) 5734 [hep-ph/9503334] [INSPIRE].
B. Bergerhoff, D. Litim, S. Lola and C. Wetterich, Phase transition of N component superconductors, Int. J. Mod. Phys.A 11 (1996) 4273 [cond-mat/9502039] [INSPIRE].
H. Gies, Running coupling in Yang-Mills theory: a flow equation study, Phys. Rev.D 66 (2002) 025006 [hep-th/0202207] [INSPIRE].
T.R. Morris, An Exact RG formulation of quantum gauge theory, Int. J. Mod. Phys.A 16 (2001) 1899 [hep-th/0102120] [INSPIRE].
S. Arnone, Y.A. Kubyshin, T.R. Morris and J.F. Tighe, Gauge invariant regularization via SU(N |N ), Int. J. Mod. Phys.A 17 (2002) 2283 [hep-th/0106258] [INSPIRE].
S. Arnone, A. Gatti and T.R. Morris, A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory, Phys. Rev.D 67 (2003) 085003 [hep-th/0209162] [INSPIRE].
S. Arnone, T.R. Morris and O.J. Rosten, A generalised manifestly gauge invariant exact renormalisation group for SU(N ) Yang-Mills, Eur. Phys. J.C 50 (2007) 467 [hep-th/0507154] [INSPIRE].
C. Wetterich, Gauge-invariant fields and flow equations for Yang–Mills theories, Nucl. Phys.B 934 (2018) 265 [arXiv:1710.02494] [INSPIRE].
S. Asnafi, H. Gies and L. Zambelli, BRST invariant RG flows, Phys. Rev.D 99 (2019) 085009 [arXiv:1811.03615] [INSPIRE].
Y. Igarashi, K. Itoh and T.R. Morris, BRST in the exact renormalization group, Prog. Theor. Exp. Phys.103 (2019) B01.
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett.B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Westview Press, Boulder, U.S.A. (1995).
G. Fejos and T. Hatsuda, Flows of multicomponent scalar models with U (1) gauge symmetry, Phys. Rev.D 100 (2019) 036007 [arXiv:1905.04272] [INSPIRE].
D.F. Litim, Optimized renormalization group flows, Phys. Rev.D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].
K. Iida, T. Matsuura, M. Tachibana and T. Hatsuda, Melting pattern of diquark condensates in quark matter, Phys. Rev. Lett.93 (2004) 132001 [hep-ph/0312363] [INSPIRE].
K. Iida, T. Matsuura, M. Tachibana and T. Hatsuda, Thermal phase transitions and gapless quark spectra in quark matter at high density, Phys. Rev.D 71 (2005) 054003 [hep-ph/0411356] [INSPIRE].
T. Hatsuda, M. Tachibana, N. Yamamoto and G. Baym, New critical point induced by the axial anomaly in dense QCD, Phys. Rev. Lett.97 (2006) 122001 [hep-ph/0605018] [INSPIRE].
N. Yamamoto, M. Tachibana, T. Hatsuda and G. Baym, Phase structure, collective modes and the axial anomaly in dense QCD, Phys. Rev.D 76 (2007) 074001 [arXiv:0704.2654] [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at m(H ) larger or equal to m(W )?, Phys. Rev. Lett.77 (1996) 2887 [hep-ph/9605288] [INSPIRE].
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ArXiv ePrint: 1908.03535
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Fejős, G., Yamamoto, N. Functional renormalization group approach to color superconducting phase transition. J. High Energ. Phys. 2019, 69 (2019). https://doi.org/10.1007/JHEP12(2019)069
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DOI: https://doi.org/10.1007/JHEP12(2019)069