Renormalization of quantum gravity coupled with matter in three dimensions

Details Renormalization of quantum gravity coupled with matter in three dimensions Renormalization of quantum gravity coupled with matter in three dimensions

2003-09-27

arxiv.org/abs/hep-th/0309249v3

Nucl.Phys. B687 (2004) 143-160

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 3 figures; references added, NPB version

Scientific paper

10.1016/j.nuclphysb.2004.03.023

In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections, but are not sufficiently powerful to ensure finiteness. Therefore, it is necessary to perform an explicit (two-loop) computation in a specific model. I consider quantum gravity coupled with Chern-Simons U(1) gauge theory and massless fermions and show that renormalization originates four-fermion divergent vertices at the second loop order. I conclude that quantum gravity coupled with matter, as it stands, is not finite in three spacetime dimensions.

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