Duality covariant quantum field theory on noncommutative Minkowski space

TL;DR

This paper demonstrates that a scalar quantum field theory on noncommutative Minkowski space exhibits UV/IR duality covariance, using resonance expansions and a two-matrix model to ensure unitarity and CT-invariance, extending Grosse-Wulkenhaar models to Minkowski signature.

Contribution

It introduces a covariant quantum field theory on noncommutative Minkowski space with a novel two-matrix model formalism ensuring unitarity and duality symmetry.

Findings

Proves UV/IR duality covariance in noncommutative Minkowski space.

Develops a two-matrix model formalism for the field theory.

Extends Grosse-Wulkenhaar models to Minkowski signature.

Abstract

We prove that a scalar quantum field theory defined on noncommutative Minkowski spacetime with noncommuting momentum coordinates is covariant with respect to the UV/IR duality which exchanges coordinates and momenta. The proof is based on suitable resonance expansions of charged noncommutative scalar fields in a background electric field, which yields an effective description of the field theory in terms of a coupled complex two-matrix model. The two independent matrix degrees of freedom ensure unitarity and manifest CT-invariance of the field theory. The formalism describes an analytic continuation of the renormalizable Grosse-Wulkenhaar models to Minkowski signature.