Intermediate Field Representation for Positive Matrix and Tensor Interactions

Abstract

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

34 pages, 21 figures

References in corpus (35)

• 2D Gravity and Random Matrices
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Colored Tensor Models - a Review
• A Model of Three-Dimensional Lattice Gravity
• Group Field Theory: An overview
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Colored Group Field Theory
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• The Universe from Scratch
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Trees, forests and jungles: a botanical garden for cluster expansions
• Bosonic Colored Group Field Theory
• Scaling behaviour of three-dimensional group field theory
• The Tensor Track, III
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• How to Resum Feynman Graphs
• Constructive ${\varphi }^4$ field theory without tears
• New 1/N expansions in random tensor models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Constructive Matrix Theory
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories
• Multicritical tensor models and hard dimers on spherical random lattices
• Progress in solving a noncommutative quantum field theory in four dimensions
• Beta functions of $U(1{)}^d$ gauge invariant just renormalizable tensor models
• Addendum to "A Renormalizable 4-Dimensional Tensor Field Theory"
• Why are tensor field theories asymptotically free?
• Large $N$ Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension $d\ge 2$
• Constructive Tensor Field Theory
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Renormalizable Models in Rank $d\ge 2$ Tensorial Group Field Theory
• Inductive Approach to Loop Vertex Expansion