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Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
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abstract
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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Properties of the wormhole-dominant phase in two-dimensional quantum gravity
In the wormhole-dominant phase of a two-dimensional matrix model, the continuum disk amplitude matches pure 2D quantum gravity, and a renormalized wormhole coupling shifts the effective bulk cosmological constant.
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