Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models

Abstract

We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary rank of the group and another valid for large rank. We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood-Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore this parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation.

30 pages. arXiv admin note: text overlap with arXiv:1706.02667. Updated version to match the publication. References added

References in corpus (24)

• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
• Giant Gravitons - with Strings Attached (III)
• Counting BPS operators in N=4 SYM
• Giant Gravitons - with Strings Attached (II)
• Correlators in tensor models from character calculus
• Space-Time in the SYK Model
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Three Dimensional View of Arbitrary $q$ SYK models
• Surprisingly Simple Spectra
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Sum rules for characters from character-preservation property of matrix models
• Cut and join operator ring in Aristotelian tensor model
• Restricted Schur Polynomials and Finite N Counting
• More on the New Large $D$ Limit of Matrix Models
• Kronecker coefficients for one hook shape
• On the complexity of computing Kronecker coefficients
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps
• The co-Pieri rule for Kronecker coefficients

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• On (q,t)-deformation of Gaussian matrix model
• From Kronecker to tableau pseudo-characters in tensor models
• Complete solution to Gaussian tensor model and its integrable properties
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• An analogue of Schur functions for the plane partitions
• Chaos in Three-dimensional Higher Spin Gravity
• Spontaneous Symmetry Breaking in Tensor Theories
• W-representation of Rainbow tensor model
• Permutation invariant Gaussian 2-matrix models
• On generalized Macdonald polynomials
• Holography for Tensor models
• Backgrounds from Tensor Models: A Proposal
• The Non-melonic Sector of Tensor Models and Gravity
• Dyonic Objects and Tensor Network Representation