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  Perturbative quantum gravity with the Immirzi parameter

Benedetti, D., & Speziale, S. (2011). Perturbative quantum gravity with the Immirzi parameter. Journal of High Energy Physics, 2011: 107. doi:10.1007/JHEP06(2011)107Open Access.

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Benedetti, D.1, Author              
Speziale, S. , Author
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1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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 Abstract: We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of fermions, the situation changes in two fundamental aspects. First, non-renormalizable logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes a priori observable, and we find that it is renormalized by a four-fermion interaction generated by radiative corrections. We compute its beta function and discuss possible implications. The sign of the beta function depends on whether the Immirzi parameter is larger or smaller than one in absolute value, and the values plus or minus one are UV fixed-points (we work in Euclidean signature). Finally, we find that the Holst action is stable with respect to radiative corrections in the case of minimal coupling, up to higher order non-renormalizable interactions.

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 Dates: 2011-04-202011
 Publication Status: Published in print
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 Identifiers: arXiv: 1104.4028
DOI: 10.1007/JHEP06(2011)107Open Access
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Title: Journal of High Energy Physics
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2011 Sequence Number: 107 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: /journals/resource/111021927548002_1