# All-orders asymptotics of tensor model observables from symmetries of restricted partitions

@article{BenGeloun2022AllordersAO, title={All-orders asymptotics of tensor model observables from symmetries of restricted partitions}, author={Joseph Ben Geloun and Sanjaye Ramgoolam}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

The counting of the dimension of the space of U(N)×U(N)×U(N) polynomial invariants of a complex 3-index tensor as a function of degree n is known in terms of a sum of squares of Kronecker coefficients. For n⩽N , the formula can be expressed in terms of a sum of symmetry factors of partitions of n denoted Z3(n) , which also counts the number of bipartite ribbon graphs with n edges. We derive the large n all-orders asymptotic formula for Z3(n) making contact with high order results previously…

## References

SHOWING 1-10 OF 51 REFERENCES

### Combinatorial Physics

- Mathematics

After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main…

### On the counting of $O(N)$ tensor invariants

- Mathematics, Computer ScienceAdvances in Theoretical and Mathematical Physics
- 2020

It is revealed that the algebraic structure which organizes these invariants differs from that of the unitary invariants, and the enumeration of $O(N)$ invariants as $d-regular graphs, using permutation group techniques, gives a sum of constrained Kronecker coefficients.

### Random Tensors (Oxford

- 2016

### Counting Tensor Model Observables and Branched Covers of the 2-Sphere

- Mathematics
- 2013

Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum eld theories…

### Partition function of free conformal fields in 3-plet representation

- Mathematics
- 2017

A bstractSimplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a…

### Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems

- MathematicsSIAM J. Comput.
- 2001

The notion of a partially stable point in a reductive-group representation is introduced, which generalizes the notion of stability in geometric invariant theory due to Mumford and reduces fundamental lower bound problems in complexity theory to problems concerning infinitesimal neighborhoods of the orbits of partially stable points.

### The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension

- Mathematics
- 2012

In this paper we generalize the results of Gurau (arXiv:1011. 2726 [gr-qc], 2011), Gurau and Rivasseau (arXiv:1101.4182 [gr-qc], 2011) and derive the full 1/N expansion of colored tensor models in…

### Tensor models, Kronecker coefficients and permutation centralizer algebras

- Mathematics
- 2017

A bstractWe show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown…

### Unitary matrix models and random partitions: Universality and multi-criticality

- PhysicsJournal of High Energy Physics
- 2021

Abstract
The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the…