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Critical behavior of colored tensor models in the large \(N\) limit. (English) Zbl 1229.81222
Summary: Colored tensor models have been recently shown to admit a large \(N\) expansion, whose leading order encodes a sum over a class of colored triangulations of the \(D\)-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of \(D\)-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
83F05 Cosmology
81T27 Continuum limits in quantum field theory
82D60 Statistical mechanical studies of polymers
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