Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models

Abstract

Motivated by the close connection of tensor models to the SYK model, we use representation theory to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge invariant operators in the free theory are computed exactly. The gauge invariant operators close a ring. The structure constants of the ring are described explicitly. Finally, we construct a collective field theory description of the bosonic tensor model.

32+1 pages; v2: refs added, minor typos corrected. v3: matches JHEP version

References in corpus (19)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• AdS_4/CFT_3 Construction from Collective Fields
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Nonplanar Integrability
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Invitation to Random Tensors
• Correlators in tensor models from character calculus
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Holography as a Gauge Phenomenon in Higher Spin Duality
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• On the central charge extension of the N=4 SYM spin chain

Cited by in corpus (13)

• Dispersive SYK model: band structure and quantum chaos
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Phases Of Melonic Quantum Mechanics
• Superintegrability of Kontsevich matrix model
• On determinant representation and integrability of Nekrasov functions
• Complete solution to Gaussian tensor model and its integrable properties
• Cauchy formula and the character ring
• BPS states, conserved charges and centres of symmetric group algebras
• Generalized cut operation associated with higher order variation in tensor models
• Holography for Tensor models
• Matrix and tensor witnesses of hidden symmetry algebras
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• The Non-melonic Sector of Tensor Models and Gravity