Ultraviolet Stable Fixed Point and Scaling Relations in 2+$ε$ Dimensional Quantum Gravity

Details Ultraviolet Stable Fixed Point and Scaling Relations in 2+$ε$ Dimensional Quantum Gravity Ultraviolet Stable Fixed Point and Scaling Relations in 2+$ε$ Dimensional Quantum Gravity

1993-03-23

arxiv.org/abs/hep-th/9303123v2

Nucl.Phys. B404 (1993) 684-716

Physics

High Energy Physics

High Energy Physics - Theory

37 pages and 1 figure, UT-636, TIT/HEP-217 and YITP/U-93-07 (a sentence to print out the figure is added, which was missing in

Scientific paper

10.1016/0550-3213(93)90594-F

We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$. This may imply the existence of consistent quantum gravity theory in 3 and 4 dimensions. We compute the scaling dimensions of the relevant operators in the theory at the ultraviolet fixed point. We obtain a scaling relation between the cosmological constant and the gravitational constant, which is crucial for searching for the continuum limit in the constructive approach to quantum gravity.

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