×

Dynamical symmetry breaking in hyperbolic 4D spacetime and in extra dimensions. (English) Zbl 1228.83013

Proc. Steklov Inst. Math. 272, 88-106 (2011); reprinted from Tr. Mat. Inst. Steklova 272, 97-116 (2011).
Summary: We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic space-time \(\mathbb R\otimes H^3\) in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field \(A_5\) in the bulk. The influence of the \(A_5\)-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83E15 Kaluza-Klein and other higher-dimensional theories
81R40 Symmetry breaking in quantum theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T20 Quantum field theory on curved space or space-time backgrounds
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Y. Nambu and G. Jona-Lasinio, ”Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I,” Phys. Rev. 122, 345–358 (1961). · doi:10.1103/PhysRev.122.345
[2] Y. Nambu and G. Jona-Lasinio, ”Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II,” Phys. Rev. 124, 246–254 (1961). · doi:10.1103/PhysRev.124.246
[3] V. G. Vaks and A. I. Larkin, ”On the Application of the Methods of Superconductivity Theory to the Problem of the Masses of Elementary Particles,” Zh. Eksp. Teor. Fiz. 40(1), 282–285 (1961) [Sov. Phys. JETP 13, 192–193 (1961)]. · Zbl 0109.21701
[4] M. K. Volkov and D. Ebert, ”Four-Quark Interactions as a Common Dynamical Basis of the Sigma Model and the Vector Dominance Model,” Yad. Fiz. 36, 1265–1277 (1982) [Sov. J. Nucl. Phys. 36, 736–742 (1982)].
[5] D. Ebert and M. K. Volkov, ”Composite-Meson Model with Vector Dominance Based on U(2) Invariant Four-Quark Interactions,” Z. Phys. C 16, 205–210 (1983). · doi:10.1007/BF01571607
[6] D. Ebert and H. Reinhardt, ”Effective Chiral Hadron Lagrangian with Anomalies and Skyrme Terms from Quark Flavour Dynamics,” Nucl. Phys. B 271, 188–226 (1986). · doi:10.1016/0550-3213(86)90359-7
[7] D. Ebert, H. Reinhardt, and M. K. Volkov, ”Effective Hadron Theory of QCD,” Prog. Part. Nucl. Phys. 33, 1–120 (1994). · doi:10.1016/0146-6410(94)90043-4
[8] T. Hatsuda and T. Kunihiro, ”QCD Phenomenology Based on a Chiral Effective Lagrangian,” Phys. Rep. 247, 221–367 (1994). · doi:10.1016/0370-1573(94)90022-1
[9] D. Ebert, L. Kaschluhn, and G. Kastelewicz, ”Effective Meson-Diquark Lagrangian and Mass Formulas from the Nambu-Jona-Lasinio Model,” Phys. Lett. B 264, 420–425 (1991). · doi:10.1016/0370-2693(91)90371-V
[10] U. Vogl, ”Diquarks from a U(3)L {\(\times\)} U(3)R Invariant Quark Lagrangian,” Z. Phys. A 337, 191–196 (1990).
[11] U. Vogl and W. Weise, ”The Nambu and Jona-Lasinio Model: Its Implications for Hadrons and Nuclei,” Prog. Part. Nucl. Phys. 27, 195–272 (1991). · doi:10.1016/0146-6410(91)90005-9
[12] B. C. Barrois, ”Superconducting Quark Matter,” Nucl. Phys. B 129, 390–396 (1977). · doi:10.1016/0550-3213(77)90123-7
[13] S. C. Frautschi, ”Asymptotic Freedom and Color Superconductivity in Dense Quark Matter,” in Hadronic Matter at Extreme Energy Density: Proc. Workshop, Erice (Italy), 1978 (Plenum Press, New York, 1980), pp. 18–27.
[14] D. Bailin and A. Love, ”Superfluidity and Superconductivity in Relativistic Fermion Systems,” Phys. Rep. 107, 325–385 (1984). · doi:10.1016/0370-1573(84)90145-5
[15] M. Alford, K. Rajagopal, and F. Wilczek, ”Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD,” Nucl. Phys. B 537, 443–458 (1999). · doi:10.1016/S0550-3213(98)00668-3
[16] K. Langfeld and M. Rho, ”Quark Condensation, Induced Symmetry Breaking and Color Superconductivity at High Density,” Nucl. Phys. A 660, 475–505 (1999). · doi:10.1016/S0375-9474(99)00417-0
[17] J. Berges and K. Rajagopal, ”Color Superconductivity and Chiral Symmetry Restoration at Non-zero Baryon Density and Temperature,” Nucl. Phys. B 538, 215–232 (1999). · doi:10.1016/S0550-3213(98)00620-8
[18] T. M. Schwarz, S. P. Klevansky, and G. Papp, ”Phase Diagram and Bulk Thermodynamical Quantities in the Nambu-Jona-Lasinio Model at Finite Temperature and Density,” Phys. Rev. C 60, 055205 (1999). · doi:10.1103/PhysRevC.60.055205
[19] M. Alford, ”Color-Superconducting Quark Matter,” Ann. Rev. Nucl. Part. Sci. 51, 131–160 (2001). · doi:10.1146/annurev.nucl.51.101701.132449
[20] B. O. Kerbikov, ”Color Superconducting State of Quarks,” arXiv: hep-ph/0110197.
[21] M. G. Alford, A. Schmitt, K. Rajagopal, and T. Schäfer, ”Color Superconductivity in Dense Quark Matter,” Rev. Mod. Phys. 80, 1455–1515 (2008). · doi:10.1103/RevModPhys.80.1455
[22] I. A. Shovkovy, ”Two Lectures on Color Superconductivity,” Found. Phys. 35, 1309–1358 (2005). · Zbl 1102.81321 · doi:10.1007/s10701-005-6440-x
[23] K. G. Klimenko, ”Three-Dimensional Gross-Neveu Model at Nonzero Temperature and in an External Magnetic Field,” Teor. Mat. Fiz. 90(1), 3–11 (1992) [Theor. Math. Phys. 90, 1–6 (1992)]. · doi:10.1007/BF01018812
[24] V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, ”Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2 + 1 Dimensions,” Phys. Rev. Lett. 73, 3499–3502 (1994). · doi:10.1103/PhysRevLett.73.3499
[25] V. P. Gusynin, V. A. Miransky, and I. Shovkovy, ”Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2 + 1 Dimensions,” Phys. Rev. D 52, 4718–4735 (1995). · doi:10.1103/PhysRevD.52.4718
[26] V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, ”Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in 3 + 1 Dimensions,” Phys. Lett. B 349, 477–483 (1995). · doi:10.1016/0370-2693(95)00232-A
[27] V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, ”Dynamical Chiral Symmetry Breaking by a Magnetic Field in QED,” Phys. Rev. D 52, 4747–4751 (1995). · doi:10.1103/PhysRevD.52.4747
[28] V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, ”Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field,” Nucl. Phys. B 462, 249–290 (1996). · doi:10.1016/0550-3213(96)00021-1
[29] K. G. Klimenko, B. V. Magnitsky, and A. S. Vshivtsev, ”Three-Dimensional \((\psi \bar \psi )^2 \) Model with an External Non-Abelian Field, Temperature and a Chemical Potential,” Nuovo Cimento A 107, 439–451 (1994). · doi:10.1007/BF02831447
[30] D. Ebert and V. Ch. Zhukovsky, ”Chiral Phase Transitions in Strong Background Fields at Finite Temperature and Dimensional Reduction,” Mod. Phys. Lett. A 12, 2567–2576 (1997). · Zbl 0908.58076 · doi:10.1142/S0217732397002697
[31] D. Ebert, K. G. Klimenko, H. Toki, and V. Ch. Zhukovsky, ”Chromomagnetic Catalysis of Color Superconductivity and Dimensional Reduction,” Prog. Theor. Phys. 106, 835–849 (2001). · Zbl 0990.81771 · doi:10.1143/PTP.106.835
[32] D. Ebert, V. V. Khudyakov, V. Ch. Zhukovsky, and K. G. Klimenko, ”Influence of an External Chromomagnetic Field on Color Superconductivity,” Phys. Rev. D 65, 054024 (2002). · doi:10.1103/PhysRevD.65.054024
[33] T. Inagaki, T. Muta, and S. D. Odintsov, ”Dynamical Symmetry Breaking in Curved Spacetime: Four-Fermion Interactions,” Prog. Theor. Phys., Suppl. 127, 93–193 (1997). · doi:10.1143/PTPS.127.93
[34] E. V. Gorbar, ”Dynamical Symmetry Breaking in Spaces with a Constant Negative Curvature,” Phys. Rev. D 61, 024013 (1999). · doi:10.1103/PhysRevD.61.024013
[35] E. V. Gorbar, ”On Effective Dimensional Reduction in Hyperbolic Spaces,” Ukr. J. Phys. 54(6), 541–546 (2009).
[36] E. V. Gorbar and V. P. Gusynin, ”Gap Generation for Dirac Fermions on Lobachevsky Plane in a Magnetic Field,” Ann. Phys. 323, 2132–2146 (2008). · Zbl 1146.81030 · doi:10.1016/j.aop.2007.11.005
[37] D. Ebert, A. V. Tyukov, and V. Ch. Zhukovsky, ”Gravitational Catalysis of Chiral and Color Symmetry Breaking of Quark Matter in Hyperbolic Space,” Phys. Rev. D 80, 085019 (2009). · doi:10.1103/PhysRevD.80.085019
[38] I. Antoniadis, ”A Possible New Dimension at a Few TeV,” Phys. Lett. B 246, 377–384 (1990). · doi:10.1016/0370-2693(90)90617-F
[39] I. Antoniadis, K. Benakli, and M. Quiros, ”Production of Kaluza-Klein States at Future Colliders,” Phys. Lett. B 331, 313–320 (1994). · doi:10.1016/0370-2693(94)91058-8
[40] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, ”The Hierarchy Problem and New Dimensions at a Millimeter,” Phys. Lett. B 429, 263–272 (1998). · Zbl 1355.81103 · doi:10.1016/S0370-2693(98)00466-3
[41] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, ”Phenomenology, Astrophysics, and Cosmology of Theories with Submillimeter Dimensions and TeV Scale Quantum Gravity,” Phys. Rev. D 59, 086004 (1999). · doi:10.1103/PhysRevD.59.086004
[42] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, ”New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV,” Phys. Lett. B 436, 257–263 (1998). · Zbl 1355.81103 · doi:10.1016/S0370-2693(98)00860-0
[43] H. Abe, H. Miguchi, and T. Muta, ”Dynamical Fermion Masses under the Influence of Kaluza-Klein Fermions in Extra Dimensions,” Mod. Phys. Lett. A 15, 445–454 (2000). · doi:10.1142/S0217732300000438
[44] S. Chang, J. Hisano, H. Nakano, N. Okada, and M. Yamaguchi, ”Bulk Standard Model in the Randall-Sundrum Background,” Phys. Rev. D 62, 084025 (2000). · doi:10.1103/PhysRevD.62.084025
[45] T. Han, J. D. Lykken, and R.-J. Zhang, ”On Kaluza-Klein States from Large Extra Dimensions,” Phys. Rev. D 59, 105006 (1999). · doi:10.1103/PhysRevD.59.105006
[46] B. A. Dobrescu, ”Electroweak Symmetry Breaking as a Consequence of Compact Dimensions,” Phys. Lett. B 461, 99–104 (1999). · doi:10.1016/S0370-2693(99)00839-4
[47] H.-C. Cheng, B. A. Dobrescu, and C. T. Hill, ”Electroweak Symmetry Breaking and Extra Dimensions,” Nucl. Phys. B 589, 249–268 (2000). · doi:10.1016/S0550-3213(00)00401-6
[48] A. B. Kobakhidze, ”Top-Quark Mass in the Minimal Top-Condensation Model with Extra Dimensions,” Yad. Fiz. 64(5), 1010–1014 (2001) [Phys. At. Nucl. 64, 941–945 (2001)].
[49] N. S. Manton, ”A New Six-Dimensional Approach to the Weinberg-Salam Model,” Nucl. Phys. B 158, 141–153 (1979). · doi:10.1016/0550-3213(79)90192-5
[50] D. B. Fairlie, ”Higgs Fields and the Determination of the Weinberg Angle,” Phys. Lett. B 82, 97–100 (1979). · doi:10.1016/0370-2693(79)90434-9
[51] D. B. Fairlie, ”Two Consistent Calculations of the Weinberg Angle,” J. Phys. G 5, L55–L58 (1979). · doi:10.1088/0305-4616/5/4/002
[52] P. Forgács and N. S. Manton, ”Space-Time Symmetries in Gauge Theories,” Commun. Math. Phys. 72, 15–35 (1980). · doi:10.1007/BF01200108
[53] S. Randjbar-Daemi, A. Salam, and J. A. Strathdee, ”Spontaneous Compactification in Six-Dimensional Einstein-Maxwell Theory,” Nucl. Phys. B 214, 491–512 (1983). · doi:10.1016/0550-3213(83)90247-X
[54] R. Sundrum, ”To the Fifth Dimension and Back,” arXiv: hep-th/0508134. · Zbl 0057.35502
[55] Y. Hosotani, ”Dynamical Mass Generation by Compact Extra Dimensions,” Phys. Lett. B 126, 309–313 (1983). · doi:10.1016/0370-2693(83)90170-3
[56] Y. Hosotani, ”Dynamics of Non-integrable Phases and Gauge Symmetry Breaking,” Ann. Phys. 190, 233–253 (1989). · doi:10.1016/0003-4916(89)90015-8
[57] L. Parker and D. J. Toms, ”Renormalization-Group Analysis of Grand Unified Theories in Curved Spacetime,” Phys. Rev. D 29, 1584–1608 (1984). · doi:10.1103/PhysRevD.29.1584
[58] D. R. Brill and J. A. Wheeler, ”Interaction of Neutrinos and Gravitational Fields,” Rev. Mod. Phys. 29, 465–479 (1957). · Zbl 0078.43503 · doi:10.1103/RevModPhys.29.465
[59] J. S. Dowker, J. S. Apps, K. Kirsten, and M. Bordag, ”Spectral Invariants for the Dirac Equation on the d-Ball with Various Boundary Conditions,” Class. Quantum Grav. 13, 2911–2920 (1996). · Zbl 0860.58042 · doi:10.1088/0264-9381/13/11/007
[60] R. Camporesi and A. Higuchi, ”On the Eigenfunctions of the Dirac Operator on Spheres and Real Hyperbolic Spaces,” J. Geom. Phys. 20, 1–18 (1996). · Zbl 0865.53044 · doi:10.1016/0393-0440(95)00042-9
[61] D. Ebert, A. V. Tyukov, and V. Ch. Zhukovsky, ”Dynamical Breaking and Restoration of Chiral and Color Symmetries in the Static Einstein Universe,” Phys. Rev. D 76, 064029 (2007). · Zbl 1140.83361 · doi:10.1103/PhysRevD.76.064029
[62] A. A. Bytsenko, G. Cognola, L. Vanzo, and S. Zerbini, ”Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section,” Phys. Rep. 266, 1–126 (1996). · doi:10.1016/0370-1573(95)00053-4
[63] P. Candelas and S. Weinberg, ”Calculation of Gauge Couplings and Compact Circumferences from Self-consistent Dimensional Reduction,” Nucl. Phys. B 237, 397–441 (1984). · doi:10.1016/0550-3213(84)90001-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.