Asymptotic safety: a simple example

Abstract

We use the Gross-Neveu model in 2<d<4 as a simple fermionic example for Weinberg's asymptotic safety scenario: despite being perturbatively nonrenormalizable, the model defines an interacting quantum field theory being valid to arbitrarily high momentum scales owing to the existence of a non-Gaussian fixed point. Using the functional renormalization group, we study the UV behavior of the model in both the purely fermionic as well as a partially bosonized language. We show that asymptotic safety is realized at non-Gaussian fixed points in both formulations, the universal critical exponents of which we determine quantitatively. The partially bosonized formulation allows to make contact to the large-Nf expansion where the model is known to be renormalizable to all-orders. In this limit, the fixed-point action as well as all universal critical exponents can be computed analytically. As asymptotic safety has become an important scenario for quantizing gravity, our description of a well-understood model is meant to provide for an easily accessible and controllable example of modern nonperturbative quantum field theory.

15 pages, 9 figures, 4 tables

References in corpus (16)

• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• On the renormalization group flow of f(R)-gravity
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Fixed points of quantum gravity in extra dimensions
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• Flow Equations for the BCS-BEC Crossover
• UV fixed-point structure of the three-dimensional Thirring model
• High-accuracy scaling exponents in the local potential approximation
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Fixed points of quantum gravity in higher dimensions
• Precision check on triviality of phi^4 theory by a new simulation method
• Asymptotic safety and the gauged SU(N) nonlinear sigma-model