Noncommutative Dipole Field Theories

TL;DR

This paper introduces noncommutative dipole field theories using a new star product, exploring their mathematical structure, physical properties, symmetry breaking, and embedding in string and M-theory contexts.

Contribution

It develops the mathematical framework for noncommutative dipole field theories and analyzes their physical implications, including symmetry breaking and string theory embeddings.

Findings

Non-local field theories with no IR/UV mixing.

Lorentz symmetry is softly broken in these theories.

Possible observable CP and CPT violation.

Abstract

Assigning an intrinsic constant dipole moment to any field, we present a new kind of associative star product, the dipole star product, which was first introduced in [hep-th/0008030]. We develop the mathematics necessary to study the corresponding noncommutative dipole field theories. These theories are sensible non-local field theories with no IR/UV mixing. In addition we discuss that the Lorentz symmetry in these theories is ``softly'' broken and in some particular cases the CP (and even CPT) violation in these theories may become observable. We show that a non-trivial dipole extension of N=4, D=4 gauge theories can only be obtained if we break the SU(4) R (and hence super)-symmetry. Such noncommutative dipole extensions, which in the maximal supersymmetric cases are N=2 gauge theories with matter, can be embedded in string theory as the theories on D3-branes probing a smooth Taub-NUT space with three form fluxes turned on or alternatively by probing a space with R-symmetry twists. We show the equivalences between the two approaches and also discuss the M-theory realization.