CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 2 APRIL 2002




The KMS State of Spacetime at the Planck Scale

Igor Bogdanoff

Mathematical Physics Laboratory, CNRS UPRES A 5029,

Bourgogne University, France

(Received October 31, 2001)

We explore here the consequences of the expected thermal equilibrium of the spacetime system at the Planck scale. In the context of string theory, it is supposed that at high temperature (Planck temperature) this system is subject to a 4D $\to$ 3D dimensional reduction, the Chern-Simon term becoming dominant in the action. We then show that the spacetime must be considered as being subject to the Kubo-Martin-Schwinger (KMS) condition at the Planck scale. Therefore, in the interior of the KMS strip, i.e., from the scale $\beta$ = 0 to the scale $\beta =^\ell$Planck, the time-like direction should be viewed as complex, the two real poles being $\beta$ = 0 and $\beta =^\ell$Planck. This means that, within the limits of the KMS strip, the spacetime metric should be considered as subject to quantum fluctuations between the Lorentzian (physical) state and the Euclidean (topological) state.

PACS. 04.65.+e - Supergravity.
PACS. 02.40.Xx - Singularity theory.


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