Phase structure of renormalizable four-fermion models in spacetimes of constant curvature

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.1917· OSTI ID:278870

Elizalde, E; Leseduarte, S; Odintsov, S D; Shilnov, Y I ^[1]

---

1. Centre for Advanced Studies CEAB, CSIC, Cami de Santa Barbara, 17300 Blanes (Spain)

A number of 2D and 3D four-fermion models which are renormalizable, in the 1/{ital N} expansion, in a maximally symmetric constant curvature space are investigated. To this purpose, a powerful method for the exact study of spinor heat kernels and propagators on maximally symmetric spaces is reviewed. The renormalized effective potential is found for any value of the curvature and its asymptotic expansion is given explicitly, both for small and for strong curvature. The influence of gravity on the dynamical symmetry-breaking pattern of some U(2) flavorlike and discrete symmetries is described in detail. The phase diagram in {ital S}{sup 2} is constructed and it is shown that, for any value of the coupling constant, a curvature exists above which chiral symmetry is restored. For the case of {ital H}{sup 2}, chiral symmetry is always broken. In three dimensions, in the case of positive curvature, {ital S}{sup 3}, it is seen that curvature can induce a second-order phase transition. For {ital H}{sup 3} the configuration given by the auxiliary fields equated to zero is not a solution of the gap equation. The physical relevance of the results is discussed. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 278870
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 4 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHIRAL SYMMETRY
COUPLING CONSTANTS
CURVATURE
FERMI INTERACTIONS
PHASE DIAGRAMS
PHASE STUDIES
PHASE TRANSFORMATIONS
PROPAGATOR
QUANTUM GRAVITY
RENORMALIZATION
SPACE-TIME
SYMMETRY BREAKING
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
U-2 GROUPS