Random tensor models in the large N limit: Uncoloring the colored tensor models

TL;DR

This paper extends the large N analysis of colored tensor models to more general non-symmetric complex tensors, revealing Virasoro constraints and multicritical behaviors, thus broadening the understanding of tensor models in quantum gravity.

Contribution

It proves that large N results and continuum limits for colored tensor models also apply to non-symmetric complex tensors, removing the necessity of color as a fundamental feature.

Findings

Existence of Virasoro constraints in the large N limit.

Identification of an infinite family of multicritical points.

Generalization of continuum limit results to non-symmetric tensors.

Abstract

Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum limit accessible analytically. In this paper we prove that these results extend to the most general tensor model for a single generic, i.e. non-symmetric, complex tensor. Colors appear in this setting as a canonical book-keeping device and not as a fundamental feature. In the large N limit, we exhibit a set of Virasoro constraints satisfied by the free energy and an infinite family of multicritical behaviors with entropy exponents \gamma_m=1-1/m.