Bootstrapping Fuzzy Scalar Field Theory

TL;DR

This paper introduces a new approach to rewriting scalar field theory on fuzzy spaces as a solvable multitrace matrix model, providing explicit high-temperature expansion terms and confirming some prior theoretical constraints.

Contribution

It presents a novel method for deriving multitrace matrix models from fuzzy scalar field theories, applicable to any hermitian matrix model, with explicit calculations up to fourth order.

Findings

Confirmed constraints from previous multitrace matrix model studies

Provided explicit high-temperature expansion terms

Challenged previous assumptions about the shape of multitrace terms

Abstract

We describe a new way of rewriting the partition function of scalar field theory on fuzzy complex projective spaces as a solvable multitrace matrix model. This model is given as a perturbative high-temperature expansion. At each order, we present an explicit analytic expression for most of the arising terms; the remaining terms are computed explicitly up to fourth order. The method presented here can be applied to any model of hermitian matrices. Our results confirm constraints previously derived for the multitrace matrix model by Polychronakos. A further implicit expectation about the shape of the multitrace terms is however shown not to be true.