arXiv subjects

Hikaru Kawai

Publications and source records attributed to Hikaru Kawai.

93 records · Page 6Linked to original sources

arXiv1993

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

We formulate a renormalizable quantum gravity in $2+ε$ 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.

hep-th↗

arXiv1993

Quantum $R^2$ Gravity in Two Dimensions

Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2π(1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32π$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.

hep-th↗

arXiv1992

Scaling Exponents in Quantum Gravity near Two Dimensions

We formulate quantum gravity in $2+ε$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The renormalization of the gravitational dressed operators is studied and their anomalous dimensions are computed. The exact scaling exponents of the 2 dimensional quantum gravity are reproduced in the strong coupling regime when we take $ε\rightarrow0$ limit. The theory possesses the ultraviolet fixed point as long as the central charge $c<25$, which separates weak and strong coupling phases. The weak coupling phase may represent the same universality class with our Universe in the sense that it contains massless gravitons if we extrapolate $ε$ up to 2.

hep-th↗