Space-Time Noncommutative Field Theories And Unitarity

TL;DR

This paper investigates the unitarity properties of noncommutative scalar field theories, revealing that space-time noncommutativity leads to non-unitary theories, while space-only noncommutativity preserves unitarity, aligning with string theory insights.

Contribution

It clarifies the unitarity behavior of space-time versus space-only noncommutative field theories and connects these findings to string theory regimes.

Findings

Space-time noncommutative theories lack unitarity.

Space-only noncommutative theories are perturbatively unitary.

String theory interpretation supports these unitarity properties.

Abstract

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.