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On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity

S. Catterall·J. Kogut·R. Renken
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Abstract

We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit.

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S. Catterall, J. Kogut, R. Renken. 1994-03-16. On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity. https://doi.org/10.1103/physrevlett.72.4062

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