Gauged Nambu-Jona-Lasinio model with extra dimensions: Phase structure and renormalizability

Journal Article · Mon Nov 01 04:00:00 EST 2004 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.70.096005· OSTI ID:20705660

Gusynin, Valery P ^[1]; Hashimoto, Michio ^[2]; Tanabashi, Masaharu ^[3]; Yamawaki, Koichi ^[4]

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1. Bogolyubov Institute for Theoretical Physics, 03143, Kiev (Ukraine)
2. Department of Physics, College of Natural Science, Pusan National University, Pusan 609-735 (Korea, Republic of)
3. Department of Physics, Tohoku University, Sendai 980-8578 (Japan)
4. Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)

We investigate phase structure of the D(>4)-dimensional gauged Nambu-Jona-Lasinio (NJL) model with {delta}(=D-4) extra dimensions compactified on TeV scale, based on the improved ladder Schwinger-Dyson (SD) equation in the bulk. We assume that the bulk (dimensionless) running gauge coupling in the SD equation for the SU(N{sub c}) gauge theory with N{sub f} massless flavors is given by the truncated Kaluza-Klein effective theory and hence has a nontrivial ultraviolet fixed point (UVFP), resulting in the walking coupling. We find the critical line in the parameter space of two couplings, the gauge coupling (value fixed at the UVFP) and the (dimensionless) four-fermion coupling, which is similar to that of the gauged NJL model with fixed (walking) gauge coupling in four dimensions. It is shown that in the presence of such walking gauge interactions the four-fermion interactions become nontrivial and renormalizable even in higher dimensions, similar to the four dimensional gauged NJL model. Such a renormalizability/nontriviality holds only in the restricted region of the critical line ('nontrivial window') with the gauge coupling larger than a nonvanishing value ('marginal triviality' point), in contrast to the four dimensional case where such a renormalizability holds for all regions of the critical line except for the pure NJL point (without gauge coupling). In the nontrivial window the renormalized effective potential yields a nontrivial interaction which is conformal invariant. The existence of the nontrivial window implies 'cutoff insensitivity' of the physics prediction in spite of the ultraviolet dominance of the dynamics. In the formal limit D{yields}4, the nontrivial window shrinks to the pure NJL point but with a nontrivial condition which coincides with the known condition of the renormalizability/nontriviality of the four dimensional gauged NJL model (9/2)(1/N{sub c})<N{sub f}-N{sub c}<(9/2)N{sub c}.

• OSTI ID: 20705660
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 70; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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COMPACTIFICATION
CONFORMAL INVARIANCE
COUPLING
FERMI INTERACTIONS
FERMIONS
FLAVOR MODEL
GAUGE INVARIANCE
KALUZA-KLEIN THEORY
NONLINEAR PROBLEMS
POTENTIALS
QUANTUM FIELD THEORY
RENORMALIZATION
SCHWINGER SOURCE THEORY
SU GROUPS
TEV RANGE
ULTRAVIOLET RADIATION