Field Theory as a Matrix Model

TL;DR

This paper introduces a novel matrix model approach to four-dimensional quantum field theories, extending beyond planar limits and incorporating fermions, using quenched coordinates for a more comprehensive reduction scheme.

Contribution

It proposes a new matrix model formulation for 4D QFTs that works beyond planar approximation and includes fermions, improving upon previous reduction methods.

Findings

Validates the matrix model approach for scalar fields.

Extends reduction scheme to include fermions.

Works for finite number of fields beyond planar approximation.

Abstract

A new formulation of four dimensional quantum field theories, such as scalar field theory, is proposed as a large N limit of a special NxN matrix model. Our reduction scheme works beyond planar approximation and applies for QFT with finite number of fields. It uses quenched coordinates instead of quenched momenta of the old Eguchi-Kawai reduction known to yield correctly only the planar sector of quantum field theory. Fermions can be also included.