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

TL;DR

This paper constructs gauge invariant observables for bosonic and fermionic tensor models, computes their correlation functions exactly, and develops a collective field theory description, advancing understanding of tensor models and their holographic connections.

Contribution

It provides a complete set of gauge invariants, explicit correlation functions, and a collective field theory framework for tensor models, linking them to holography.

Findings

Gauge invariant operators form a closed ring.

Correlation functions are computed exactly in the free theory.

A collective field theory description is developed.

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.