Duality in Scalar Field Theory on Noncommutative Phase Spaces

TL;DR

This paper introduces a new duality symmetry in noncommutative scalar field theory that involves Fourier transformation and scaling, which remains valid at the quantum level and relates different parameter regimes.

Contribution

It extends known dualities to interacting noncommutative field theories with star-products, demonstrating their persistence at all orders of perturbation theory.

Findings

Duality acts via Fourier transform and scaling on fields.

Dual models often have the same form with transformed parameters.

Duality persists at the quantum level for all orders in perturbation theory.

Abstract

We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined with a star-product, of that which arises in quantum field theories of non-interacting scalar particles coupled to a constant background electromagnetic field. The dual models are in general of the same original form but with transformed coupling parameters, while in certain special cases all parameters are essentially unchanged. Using a particular regualarization we show, to all orders of perturbation theory, that that this duality also persists at the quantum level. We also point out various other properties of this class of noncommutative field theories.