Investigations of symmetry breakings by multiple condensates on exotic chiral condensed phases

Abstract

The Nambu-Goldstone modes on the exiotic chiral condensed phase with chiral and tensor-type quark-antiquark condensates are investigated by using of the two-point vertex functions. It is shown that one of the Nambu-Goldstone modes appears as a result of meson-mixing. As is well known, another method to find the Nambu-Goldstone modes is given by the use of the algebraic commutation relations between broken generators and massless modes obtained through the spontaneous symmetry breaking. This method is adopted to the cases of the chiral symmetry breakings due to the tensor-type condensate and the inhomogeneous chiral condensate. The result obtained by the use of the meson two-point vertex functions is obviously reproduced in the case of the tensor-type condensate. Furthermore, we investigate the general rules for determining the broken symmetries and the Nambu-Goldstone modes algebraically. As examples, the symmetry breaking pattern and the Nambu-Goldstone modes due to the tensor-type condensate or the inhomogeneous chiral condensate are shown by adopting the general rules developed in this paper in the algebraic method.

arXiv comment16 pages, No figure

References in corpus (17)

• Color superconductivity in dense quark matter
• Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The phase diagram of dense QCD
• Phases of Dense Quarks at Large N_c
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• Chiral symmetry and density wave in quark matter
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• The superfluid phases of quark matter: Ginzburg-Landau theory and color neutrality
• Redundancies in Nambu-Goldstone Bosons
• Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase
• Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries
• Effective Potential Approach to Quark Ferromagnetization in High Density Quark Matter
• Spin polarization and chiral symmetry breaking at finite density
• Spontaneous magnetization under a pseudovector interaction between quarks in high density quark matter
• A possibility of existence of a pseudovector-type quark-antiquark condensate in the quark matter and Nambu-Goldstone modes on that condensate in the Nambu-Jona-Lasinio model