Renormalization Group and Quantum Gravity
Sep, 198931 pages
Published in:
- Nucl.Phys.B 336 (1990) 115-145
- Published: 1990
Report number:
- UT-550-TOKYO
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Abstract: (Elsevier)
We study non-perturbative effects of the quantum fluctuation of gravity by means of the ϵ-expansion around two dimensions and the renormalization group method. By introducing the fractal dimension as an order parameter we show that the space-time possesses a self-similar structure. We also point out that an operator such as the cosmological term, the scalar and fermion mass terms ceases to exist as a local one as the number of matter fields increases. This fact may be taken as a suggestion as to how to answer the naturalness problem, in particular the vanishing of the cosmological term. It is argued that there exists potential pathology in the ϵ-expansion in the 2+ϵ dimensional gravity and we give the solution that it is a double expansion in ϵ and 1 −c where c is the number of matter fields (c=N S + 1 2 N F ) .- quantum gravity
- dimension: 2
- renormalization group: beta function
- epsilon expansion
- fermion: mass
- mass: fermion
- cosmological constant
- perturbation theory: higher-order
- fractal
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