Non-local Field Theory from Matrix Models

TL;DR

This paper introduces a non-local field theory derived from matrix models using Wigner-Weyl transformation, revealing new high-energy phenomena and unifying gauge and geometric symmetries.

Contribution

It presents a novel reformulation of matrix theories as non-local quantum field theories with Moyal product interactions, connecting to local dynamics at low energies.

Findings

Matrix theories can be reformulated as non-local field theories.

The framework unifies gauge and geometric symmetries.

Low-energy limit recovers local spacetime dynamics.

Abstract

We show that a class of matrix theories can be understood as an extension of quantum field theory which has non-local interactions. This reformulation is based on the Wigner-Weyl transformation, and the interactions take the form of Moyal product on a doubled geometry. We recover local dynamics on the spacetime as a low-energy limit. This framework opens up the possibility for studying novel high-energy phenomena, including the unification of gauge and geometric symmetries in a gauge theory.