Finite-$N$ Bootstrap Constraints in Matrix and Tensor Models

TL;DR

This paper applies matrix bootstrap techniques to finite-$N$ matrix and tensor models, deriving bounds on expectation values and two-point functions that depend on model parameters.

Contribution

It demonstrates how bootstrap methods can constrain finite-$N$ matrix and tensor models, revealing bounds that depend on model properties and parameters.

Findings

Bounds in matrix models depend on multi-trace expectation values, not explicitly on N.

Tensor models allow bounds that vary with N, exploring broader parameter space.

New bounds on two-point functions as a function of quartic coupling in tensor models.

Abstract

We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models, we find further evidence that bounds do not depend explicitly on $N$, but rather on properties of multi-trace expectation values. For tensor models, the structure of the Schwinger-Dyson equations allow for bounds that vary as a function of $N$, admitting a broader scan of the parameter space of the theory. In the latter case, we find novel bounds on the two-point function as a function of the quartic coupling of the theory.