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The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity and the precise conditions allowing to associate a four-dimensional simplicial manifold to Feynman diagrams of a rank-four tensor model.
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribut
We have analyzed IIB matrix model based on the improved mean field approximation (IMFA) and have obtained a clue that the four-dimensional space-time appears as its most stable vacuum. This method is a systematic way to give an improved perturbation
Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In
For the purpose of analyzing non-perturbative dynamics of string theory, Nishimura and Sugino have applied an improved mean field approximation (IMFA) to IIB matrix model. We have extracted the essence of the IMFA and obtained a general scheme, an im
We revisit the issue of worldline formulations for the q-state Potts model and discuss a worldline representation in arbitrary dimensions which also allows for magnetic terms. For vanishing magnetic field we implement a Hodge decomposition for resolv