Renormalization group flows in a Lifshitz-like four-Fermi model

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.085005· OSTI ID:21409632

Dhar, Avinash; Mandal, Gautam; Nag, Partha ^[1]

---

1. Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005 (India)

We study renormalization group flows in the Lifshitz-like N-flavor four-Fermi model discussed in [Phys. Rev. D 80, 105018 (2009)]. In the large-N limit, a nontrivial flow occurs in only one of all possible marginal couplings and one relevant coupling, which provides the scale for Lorentz invariance violations. We discuss in detail the phase diagram and renormalization group flows in the space of couplings, which includes the Lifshitz fixed point, the free field fixed point and a new fixed point characterized by z=1 scaling and a violation of Lorentz invariance, which cannot be tuned away by adjusting a parameter. In the broken symmetry phase, the model flows from the z=3 Lifshitz-like fixed point in the ultraviolet to this new fixed point in the infrared. However, in a modified version of the present model, which has an effective ultraviolet cutoff much smaller than the Lorentz invariance violating scale, the infrared behavior is governed by an approximately Lorentz invariant theory, similar to the low-energy limit of the usual relativistic Nambu-Jona-Lasinio model. Such a modified model could be realized by a supersymmetric version of the present model, if it exists.

• OSTI ID: 21409632
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.085005; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING
FLAVOR MODEL
FLOW MODELS
LORENTZ INVARIANCE
PHASE DIAGRAMS
RELATIVISTIC RANGE
RENORMALIZATION
SCALING
SIMULATION
SPACE
SUPERSYMMETRY
SYMMETRY BREAKING
ULTRAVIOLET RADIATION
COMPOSITE MODELS
DIAGRAMS
ELECTROMAGNETIC RADIATION
ENERGY RANGE
INFORMATION
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
RADIATIONS
SYMMETRY