Intermediate Field Representation for Positive Matrix and Tensor\n Interactions

2016/09/16 by Luca Lionni, Lionni, Luca, Vincent Rivasseau +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1609.05018

openalex publication_date 2016/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce an intermediate field representation for random\nmatrices and random tensors with positive (stable) interactions of degree\nhigher than 4. This representation respects the symmetry axis responsible for\npositivity. It is non-perturbative and allows to prove that such models are\nBorel-Le Roy summable of the appropriate order in their coupling constant.\nHowever we have not been able yet to associate a convergent Loop Vertex\nExpansion to this representation, hence our Borel summability result is not of\nthe optimal expected form when the size N of the matrix or of the tensor tends\nto infinity.\n

Citations

• A planar diagram theory for strong interactions
• Renormalizable Models in Rank d≥ 2 Tensorial Group Field Theory

Related

• An equivalence in random matrix and tensor models via a dually weighted intermediate field representation
• Tensor models with generalized melonic interactions
• A New Large N Expansion for General Matrix-Tensor Models
• Random Tensor models: Combinatorics, Geometry, Quantum Gravity and Integrability
• Notes on Tensor Models and Tensor Field Theories