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KMS space-time at the Planck scale

Considering the expected thermal equilibrium of the space-time at the Planck scale, we suggest here that this system should globally be considered as subject to the Kubo-Martin-Schwinger (KMS) condition at such a scale. Consequently, within the limits of the KMS strip, i.e. from the scale β = 0 to the scale β = P l a n c k , the time-like direction should be viewed as complex, the two real poles being β = 0 and β = P l a n c k . This means that in the interior of the KMS strip, the space-time metric should be considered as subject to quantum fluctuations between the Lorentzian (physical) state and the dual Euclidean (topological) state. Such an approach appears as a consequence of the dualities explored in the context of string theory.