Asymptotic safety: A simple example

Jens Braun, Holger Gies, and Daniel D. Scherer
Phys. Rev. D 83, 085012 – Published 11 April 2011

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.

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  • Received 14 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.085012

© 2011 American Physical Society

Authors & Affiliations

Jens Braun, Holger Gies, and Daniel D. Scherer

  • Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany

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Issue

Vol. 83, Iss. 8 — 15 April 2011

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