Abstract
Using results of statistical field theory for systems with an anisotropic disorder, we present an analog model for Euclidean wormholes and topological fluctuation effects in a Riemannian space [Formula: see text]. The contribution of wormholes and topological fluctuations to the Euclidean gravitational functional integral is modeled by quenched randomness defined in the [Formula: see text] manifold. We obtain a disorder-averaged free energy by taking the average over all the realizations of the random fields. In the scenario of topology fluctuation, there appears a superposition of infinite branes that contribute to the physical quantities. All topology fluctuations can be understood as two distinct kinds of Euclidean wormholes: wormholes confined to one brane, and wormholes connecting different branes.
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