Quantum gravity, torsion, parity violation, and all that

Laurent Freidel, Djordje Minic, and Tatsu Takeuchi
Phys. Rev. D 72, 104002 – Published 1 November 2005

Abstract

We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective Lagrangian which turns out to involve two parameters: one measuring the nonminimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of nonminimal coupling the effective Lagrangian contains an axial-vector interaction leading to parity violation. Alternatively, in the case of minimal coupling there is no parity violation and the effective Lagrangian contains only the usual axial-axial interaction. In this situation the real values of the Immirzi parameter are not at all constrained. On the other hand, purely imaginary values of the Immirzi parameter lead to violations of unitarity for the case of nonminimal coupling. Finally, the effective Lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.

  • Received 16 September 2005

DOI:https://doi.org/10.1103/PhysRevD.72.104002

©2005 American Physical Society

Authors & Affiliations

Laurent Freidel1,2,*, Djordje Minic3,†, and Tatsu Takeuchi3,‡

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline St. N. Waterloo, N2L 2Y5, Ontario, Canada
  • 2Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon, Cedex 07, France
  • 3Institute for Particle Physics and Astrophysics, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA

  • *Electronic address: lfreidel@perimeterinstitute.ca
  • Electronic address: dminic@vt.edu
  • Electronic address: takeuchi@vt.edu

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Issue

Vol. 72, Iss. 10 — 15 November 2005

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