2009/11/27 by Avinash Dhar, Gautam Mandal, Partha Nag
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1103/physrevd.81.085005
published as Phys.Rev.D81:085005,2010 · 30 pages, 2 figures
arxiv created 2009/11/27 · openalex publication_date 2010/04/06 · arxiv updated 2010/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.