Asymptotic safety: A simple example
- Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)
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-N{sub f} 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.
- OSTI ID:
- 21541532
- Journal Information:
- Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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