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

By Valentin Bonzom, R. Gurau, Vincent Rivasseau. 2012

290 citations recorded by the source corpus.

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 m = 1 1/m.

Subfields: Computational Mathematics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e97865f17eaa6cd68d4d5a6ba1e20bf3e03f9841

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Sylvain Carrozza
2. Adrian Tanasa
3. G. Tarnopolsky
4. I. Klebanov
5. R. Gurau
6. Vincent Rivasseau

In Nuclear and High Energy Physics

1. A. Eichhorn
2. Sylvain Carrozza
3. Adrian Tanasa
4. G. Tarnopolsky
5. W. Metzner
6. M. Tissier
7. N. Dupuis
8. N. Wschebor

In Statistical and Nonlinear Physics

1. Sylvain Carrozza
2. Adrian Tanasa
3. I. Klebanov
4. G. Tarnopolsky
5. A. Eichhorn
6. L. Canet
7. W. Metzner
8. N. Dupuis

Citations in the corpus

• O(N) Random Tensor Models (2015, methodology): “Let us recall that, in the tensor model framework, one calls these invariants bubbles and they are vertices of the QFT model to be considered (see for example [9] for details on this type of construction).”
• Universality for Random Tensors (2011, background): “For the case of perturbed Gaussian measures the large N covariance is a sum over an infinite family of Feynman graphs and exhibits various multicritical behaviors [6].”
• Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, background): “In uncolored models with complex tensors, which were studied in [13], each index loop necessarily passed through an even number of vertices, but in models with real tensors a loop can also pass through an odd number of vertices.”
• The nonperturbative functional renormalization group and its applications (2020, background): “The connection to quantum gravity arises as the Feynman diagrams of such rank-d models are dual to triangulations of d dimensional space, see [1338–1343], see [1344–1350] for reviews.”