General Properties of Noncommutative Field Theories

TL;DR

This paper investigates fundamental properties of noncommutative field theories derived from string theory, proving the CPT theorem, analyzing spin-statistics, and examining phenomenological implications, highlighting their theoretical consistency and limitations.

Contribution

It extends the Wightman axioms to noncommutative theories, proves the CPT theorem for space-space noncommutativity, and constructs a UV/IR safe low-energy effective action for noncommutative N=4, U(1) gauge theory.

Findings

CPT theorem holds for space-space noncommutative theories.

Noncommutative N=4, U(1) gauge theory can be softly broken with a UV/IR safe effective action.

Phenomenological prospects of such theories are limited.

Abstract

In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommutativity. We analyze as well questions associated to the spin-statistics connections, and show that noncommutative N=4, U(1) gauge theory can be softly broken to N=0 satisfying the axioms and providing an example where the Wilsonian low energy effective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative.