Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-07-15
JHEP 0212 (2002) 066
Physics
High Energy Physics
High Energy Physics - Theory
67 pages, Latex; v3: improved discussion of stationary sector; agrees with published version
Scientific paper
10.1088/1126-6708/2002/12/066
A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be achieved in a space of Lagrangians differing only by a field dependent conformal factor. In particular the Noether currents and the quantum constraints can be defined as finite composite operators. The form of the field dependence in the conformal factor changes with the renormalization scale and a closed formula is obtained for the beta functional governing its flow. The flow possesses a unique fixed point at which the trace anomaly is shown to vanish. The approach to the fixed point adheres to Weinberg's ``asymptotic safety'' scenario, both in the gravitational wave/cosmological sector and in the stationary sector.
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