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Topological Characteristics of Random Surfaces Generated by Cubic Interactions

Nicholas Pippenger·Kristin Schleich
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Abstract

We consider random topologies of surfaces generated by cubic interactions. Such surfaces arise in various contexts in 2-dimensional quantum gravity and as world-sheets in string theory. Our results are most conveniently expressed in terms of a parameter h = n/2 + χ, where n is the number of interaction vertices and χis the Euler characteristic of the surface. Simulations and results for similar models suggest that Ex[h] = log (3n) + γ+ O(1/n) and Var[h] = log (3n) + γ- π^2/6 + O(1/n). We prove rigourously that Ex[h] = log n + O(1) and Var[h] = O(log n). We also derive results concerning a number of other characteristics of the topology of these random surfaces.

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Nicholas Pippenger, Kristin Schleich. 2003-06-11. Topological Characteristics of Random Surfaces Generated by Cubic Interactions. https://arxiv.org/abs/gr-qc/0306049

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