Ward identities and combinatorics of rainbow tensor models

Abstract

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

48 pages

References in corpus (35)

• A Perturbative Window into Non-Perturbative Physics
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The Bulk Dual of SYK: Cubic Couplings
• The complete $1/N$ expansion of a SYK--like tensor model
• Group field theory renormalization - the 3d case: power counting of divergences
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Scaling behaviour of three-dimensional group field theory
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Instantons and Merons in Matrix Models
• Generation of Matrix Models by W-operators
• On KP-integrable Hurwitz functions
• EPRL/FK Group Field Theory
• Lost in Translation: Topological Singularities in Group Field Theory
• On the complete perturbative solution of one-matrix models
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Vector models and generalized SYK models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Intersection theory from duality and replica
• Comments on 2D dilaton gravity system with a hyperbolic dilaton potential
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Introduction to Non-Linear Algebra
• Topology in colored tensor models via crystallization theory
• Wall Crossing Invariants: from quantum mechanics to knots
• Bi-Local Holography in the SYK Model: Perturbations
• Partition function of free conformal fields in 3-plet representation
• Intersection numbers of Riemann surfaces from Gaussian matrix models
• Check-Operators and Quantum Spectral Curves

Cited by in corpus (59)

• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Spectra of Operators in Large $N$ Tensor Models
• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Space-Time in the SYK Model
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• SYK-like Tensor Models on the Lattice
• On (q,t)-deformation of Gaussian matrix model
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Contrasting SYK-like Models
• Superintegrability of Kontsevich matrix model
• Sum rules for characters from character-preservation property of matrix models
• Cut and join operator ring in Aristotelian tensor model
• Interpolating Matrix Models for WLZZ series
• On matrix models and their $q$-deformations
• Towards a Finite-$N$ Hologram
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• On determinant representation and integrability of Nekrasov functions
• From Kronecker to tableau pseudo-characters in tensor models
• Non-Abelian W-representation for GKM
• Matrix model partition function by a single constraint
• Complete solution to Gaussian tensor model and its integrable properties
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• Melonic Dominance in Subchromatic Sextic Tensor Models
• An analogue of Schur functions for the plane partitions
• Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model
• Position Space Equations for Banana Feynman Diagrams
• Cauchy formula and the character ring
• Generalized Q-functions for GKM
• Bilinear character correlators in superintegrable theory
• Orthogonal Polynomials in Mathematical Physics
• Tensorial generalization of characters
• Flowing in discrete gravity models and Ward identities: A review
• Two $\beta$-ensemble realization of $\beta$-deformed WLZZ models
• Spontaneous Symmetry Breaking in Tensor Theories
• W-representations of the fermionic matrix and Aristotelian tensor models
• W-representation of Rainbow tensor model
• Generalized cut operation associated with higher order variation in tensor models
• Complete Solution of a Gauged Tensor Model
• Harer-Zagier formulas for knot matrix models
• On generalized Macdonald polynomials
• Correspondence between Feynman diagrams and operators in quantum field theory that emerges from tensor model
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector
• Superintegrability and Kontsevich-Hermitian relation
• From Hurwitz numbers to Feynman diagrams: counting rooted trees in log gravity
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Backgrounds from Tensor Models: A Proposal
• Phases in WLZZ Matrix Models
• Review on the Operator/Feynman diagram/Dessins d'enfant Correspondence in Tensor Model
• Itzykson-Zuber correlators from character expansion
• A new kind of anomaly: on W-constraints for GKM
• Proving superintegrability in $\beta$-deformed eigenvalue models
• Integrability and Matrix Models