Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion

Abstract

We discuss the Nambu-Jona-Lasinio (NJL) model in curved space-time with torsion in the leading order of the $1/N$ expansion. The effective potential of the torsion sector is calculated using the new technique based on the nonlocal part of anomaly-induced action which was recently found to produce the effective potential in the low-energy limit. The spontaneous symmetry breaking caused by the change of the torsion term is found, confirming the statements known from the existing literature. Furthermore, the gap equation is calculated as a function of curvature and torsion. Finally, the behavior of the effective four fermions coupling constant as a function of the torsion is discussed.

In this third version, we extended the discussions, added new explanations, the graphics were redone, and we added new conclusions. 20 pages and 5 figures. Fits the published version

References in corpus (8)

• Effective Action of Vacuum: Semiclassical Approach
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Macroscopic Effects of the Quantum Trace Anomaly
• Quantum Effects in Softly Broken Gauge Theories in Curved Space-Times
• Einstein-Cartan Portal to Dark Matter
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Remarks on Barbero-Immirzi parameter as a field
• Covariant spin-parity decomposition of the Torsion and Path Integrals