Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-07-26
Phys.Rev.D72:104002,2005
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, LaTeX; (two footnotes, acknowledgements and references added, typos corrected)
Scientific paper
10.1103/PhysRevD.72.104002
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 non-minimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of non-minimal 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 non-minimal coupling. Finally, the effective lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.
Freidel Laurent
Minic Djordje
Takeuchi Tatsu
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