O(N) Random Tensor Models

By Sylvain Carrozza, Adrian Tanasa. 2015

184 citations recorded by the source corpus.

We define in this paper a class of three-index tensor models, endowed with $${O(N)^{\otimes 3}}$$O(N)⊗3 invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ba3c566af4ea787daa96ed42199358cce75322a0

How researchers see this paper

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In Atomic and Molecular Physics, and Optics

1. G. Tarnopolsky
2. I. Klebanov
3. T. Takayanagi

In Computational Mathematics

1. G. Tarnopolsky
2. I. Klebanov

In Statistics and Probability

1. G. Tarnopolsky
2. I. Klebanov

Citations in the corpus

• Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, background): “The arguments in this section, which are analogous to those in [31], apply to the uncolored models with O(N)(3) symmetry, both in the fermionic and bosonic cases and for any d.”