  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.
