Matrix and tensor witnesses of hidden symmetry algebras

Abstract

Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the combinatorics of large $N$ gauge theories and matrix models with manifest continuous gauge symmetries. Polynomial functions invariant under the manifest symmetries are the observables of interest and have applications in AdS/CFT. We compute such correlators in the presence of matrix or tensor witnesses, which by definition, can include a matrix or tensor field appearing as a coupling in the action (i.e a spurion) or as a classical (un-integrated) field in the observables, appearing alongside quantum (integrated) fields. In both matrix and tensor cases we find that two-point correlators of general gauge-invariant observables can be written in terms of gauge invariant functions of the witness fields, with coefficients given by structure constants of the associated PCAs. Fourier transformation on the relevant PCAs, relates combinatorial bases to representation theoretic bases. The representation theory basis elements obey orthogonality results for the two-point correlators which generalise known orthogonality relations to the case with witness fields. The new orthogonality equations involve two representation basis elements for observables as input and a representation basis observable constructed purely from witness fields as the output. These equations extend known equations in the super-integrability programme initiated by Mironov and Morozov, and are a direct physical realization of the Wedderburn-Artin decompositions of the hidden permutation centralizer algebras of matrix/tensor models.

arXiv comment53 pages + Appendices, 9 Figures

References in corpus (48)

• Gauge Theory Correlators from Non-Critical String Theory
• A Large-N Reduced Model as Superstring
• Bubbling AdS space and 1/2 BPS geometries
• Giant Gravitons in Conformal Field Theory
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• The 1/N expansion of colored tensor models
• 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
• D-branes in Yang-Mills theory and Emergent Gauge Symmetry
• Open Strings from N=4 Super Yang-Mills
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Giant Gravitons - with Strings Attached (III)
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• Exact Multi-Restricted Schur Polynomial Correlators
• Giant Gravitons - with Strings Attached (I)
• Holographic three-point functions of giant gravitons
• Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory
• On the complete perturbative solution of one-matrix models
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Multi-matrix models and emergent geometry
• A double coset ansatz for integrability in AdS/CFT
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Integrability vs. Information Loss: A Simple Example
• Superintegrability summary
• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Extremal vs. Non-Extremal Correlators with Giant Gravitons
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Giant gravitons and correlators
• Restricted Schur Polynomials and Finite N Counting
• Absorption of closed strings by giant gravitons
• Permutation Centralizer Algebras and Multi-Matrix Invariants
• Complex matrix model duality
• Orthogonal Bases of Invariants in Tensor Models
• BPS coherent states and localization
• On the Regularization of Extremal Three-point Functions Involving Giant Gravitons
• Multi-matrix models at general coupling
• BPS states, conserved charges and centres of symmetric group algebras
• Fermions on curved backgrounds of matrix models
• Quarter-BPS states, multi-symmetric functions and set partitions
• CFT4 as SO(4,2)-invariant TFT2
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
• Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction
• Generating Functions for Giant Graviton Bound States
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models

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