Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature

Abstract

By using the Nambu-Jona-Lasinio model, we study dynamical symmetry breaking in spaces with constant negative curvature. We show that the physical reason for zero value of critical coupling value $g_c=0$ in these spaces is connected with the effective reduction of dimension of spacetime $1+D\to 1+1$ in the infrared region, which takes place for any dimension $1+D$. Since the Laplace-Beltrami operator has a gap in spaces with constant negative curvature, such an effective reduction for scalar fields is absent and there are not problems with radiative corrections due to scalar fields. Therefore, dynamical symmetry breaking with the effective reduction of the dimension of spacetime for fermions in the infrared region is consistent with the Mermin-Wagner-Coleman theorem, which forbids spontaneous symmetry breaking in (1 + 1)-dimensional spacetime.

minor text changes, added new references

References in corpus (1)

• Gauge Theory Correlators from Non-Critical String Theory

Cited by in corpus (21)

• Analogy between rotation and density for Dirac fermions in a magnetic field
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Renormalization group flow and symmetry restoration in de Sitter space
• Universal properties of the near-horizon optical geometry
• Pion, sigma-meson and diquarks in the 2SC phase of dense cold quark matter
• Chiral gap effect in curved space
• A curvature bound from gravitational catalysis
• Pion condensation of quark matter in the static Einstein universe
• Mesons and diquarks in the color neutral 2SC phase of dense cold quark matter
• On the thermodynamics of the 2+1 dimensional Gross-Neveu model with complex chemical potential
• A curvature bound from gravitational catalysis in thermal backgrounds
• Gravitational instantons and anomalous chiral symmetry breaking
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• Geometrically induced magnetic catalysis and critical dimensions
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space
• Mesons and diquarks in neutral color superconducting quark matter with $\beta$-equilibrium
• Curvature and topological effects on dynamical symmetry breaking in a four- and eight-fermion interaction model
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Chiral Phase Structure at Finite Temperature and Density in Einstein Universe
• Color superconductivity in the static Einstein Universe
• Fate of chiral symmetry in Riemann-Cartan geometry