Noncommutative Dipole Field Theories

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 [hepth/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.