Enhanced symmetries of gauge theory and resolving the spectrum of local operators

Abstract

Enhanced global non-abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalising the two-point functions of multi-matrix operators. Generalised Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalise the two-point function. For the case of U (N) gauge theory with a single complex matrix in the adjoint of the gauge group we have a U(N)^{\times 4} global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-anti-brane systems. More generally these remarks can be extended to the diagonalisation for any global symmetry group G. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.

arXiv comment45 pages, no figures. Revised version : added refs, corrected typos

References in corpus (32)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• AdS3 Black Holes and a Stringy Exclusion Principle
• Bubbling AdS space and 1/2 BPS geometries
• Matrix String Theory
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Two Dimensional QCD is a String Theory
• A toy model for the AdS/CFT correspondence
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• The Library of Babel: On the origin of gravitational thermodynamics
• 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
• From Free Fields to $AdS$
• D-branes in Yang-Mills theory and Emergent Gauge Symmetry
• Free Large N Supersymmetric Yang-Mills Theory as a String Theory
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Exact Multi-Restricted Schur Polynomial Correlators
• Giant Gravitons - with Strings Attached (I)
• Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory
• Finite in All Directions
• Non commutative gravity from the ADS/CFT correspondence
• Integrability vs. Information Loss: A Simple Example
• Schur-Weyl duality as an instrument of Gauge-String duality
• Permutations and the Loop
• Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills
• Quantum Spacetimes and Finite N Effects in 4D Super Yang-Mills Theories
• A New Approach to the Representation Thoery of the Symmetric Groups. 2

Cited by in corpus (50)

• Nonplanar Integrability
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• Surprisingly Simple Spectra
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• From Large N Nonplanar Anomalous Dimensions to Open Spring Theory
• Partition Functions for Higher-Spin theories in AdS
• Emergent Threebrane Lattices
• Restricted Schur Polynomials for Fermions and integrability in the su(2|3) sector
• Correlators in Nontrivial Backgrounds
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Restricted Schur Polynomials and Finite N Counting
• Correlation functions and representation bases in free N=4 Super Yang-Mills
• Permutation Centralizer Algebras and Multi-Matrix Invariants
• Cut-and-join operators and N=4 super Yang-Mills
• Correlators Of Operators with a Large R-charge
• Efficient multi port-based teleportation schemes
• Nonplanar Integrability: Beyond the SU(2) Sector
• Free particles from Brauer algebras in complex matrix models
• Operator Mixing and the AdS/CFT correspondence
• BPS states, conserved charges and centres of symmetric group algebras
• BPS operators in $\mathcal{N}=4$ $SO(N)$ super Yang-Mills theory: plethysms, dominoes and words
• Exciting LLM Geometries
• Multi-matrix models and Noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• Integrable Subsectors from Holography
• Flavour singlets in gauge theory as Permutations
• Quarter-BPS states, multi-symmetric functions and set partitions
• Integrality, Duality and Finiteness in Combinatoric Topological Strings
• Central Charges for the Double Coset
• Laplacians in polar matrix coordinates and radial fermionization in higher dimensions
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• The quantum detection of projectors in finite-dimensional algebras and holography
• Scrambling in Yang-Mills
• Negative anomalous dimensions in N=4 SYM
• Permutation invariant Gaussian 2-matrix models
• Subleading corrections to the Double Coset Ansatz preserve integrability
• Quantum Information Processing and Composite Quantum Fields
• Graph duality as an instrument of Gauge-String correspondence
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
• Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
• Anomalous dimensions from boson lattice models
• Semiclassical SL(2) Strings on LLM backgrounds
• Noncommutative Frobenius algebras and open-closed duality
• De Alfaro, Fubini and Furlan from multi Matrix Systems
• Matrix and tensor witnesses of hidden symmetry algebras
• Non-planar operator mixing by Brauer representations
• Interacting Double Coset Magnons
• Interacting Emergent Yang-Mills theory
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• Large N anomalous dimensions for large operators in Leigh-Strassler deformed SYM