Permutation invariant Gaussian 2-matrix models

Abstract

We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A correspondence is established between the permutation invariant polynomial functions of the matrix variables (the observables of the model) and directed colored graphs, which sheds light on stability properties in the large $D$ counting of these invariants. The refined counting of the graphs is given in terms of double cosets involving permutation groups defined by the local structure of the graphs. Linear and quadratic observables are transformed to an $S_D$ representation theoretic basis and are used to define the convergent Gaussian measure. The perturbative rules for the computation of expectation values of graph-basis observables of any degree are given in terms of the representation theoretic parameters. Explicit results for a number of observables of degree up to four are given along with a Sage programme that computes general expectation values.

arXiv comment80 pages, 11 figures

References in corpus (32)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Dirichlet-Branes and Ramond-Ramond Charges
• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Bound States Of Strings And $p$-Branes
• AdS3 Black Holes and a Stringy Exclusion Principle
• Drag force in AdS/CFT
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Giant Gravitons in Conformal Field Theory
• The 1/N expansion of colored tensor models in arbitrary dimension
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Exact Multi-Matrix Correlators
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• String Theory in Two Dimensions
• Energy flow polynomials: A complete linear basis for jet substructure
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• Exact Multi-Restricted Schur Polynomial Correlators
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• A double coset ansatz for integrability in AdS/CFT
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Recursive Graphical Construction of Feynman Diagrams and Their Multiplicities in phi^4- and in phi^2A-Theory
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Cut and join operator ring in Aristotelian tensor model
• Strings from Feynman Graph counting : without large N
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• On the refined counting of graphs on surfaces
• Permutation Invariant Gaussian Matrix Models
• Using Sentence Plausibility to Learn the Semantics of Transitive Verbs
• Testing the Gaussianity and Statistical Isotropy of the Universe
• A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in ${\varphi }^4$ theory
• Gaussianity and typicality in matrix distributional semantics

Cited by in corpus (3)

• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
• Generating Functions for Giant Graviton Bound States