Galilean Kalb-Ramond Field

Abstract: In this paper, we build the Galilean limit of the free Kalb-Ramond two-form and also study the symmetries. Two different methods are discussed. The first is an Inönü-Wigner contraction. In this method, we take the scaling of space-time coordinates and the two-form field. The relativistic equations boil down to two inequivalent limits, electric and magnetic. In both, the equations of motion come out to be invariant under the full infinite-dimensional Galilean conformal algebra precisely in D=6. The second method is the null-reduction. In this, we start from a theory in D+1 dimensions and end up with a theory in D dimensions. This method yields a local Galilean Lagrangian. Here, the action is invariant under the global generators (boosts, rotations, translations and scale transformations) but not under higher Witt modes of the Galilean conformal algebra. We also calculate the two-point functions in both constructions from the boost, scale and rotation Ward identities, and by exhibiting the truncation that maps the null-reduction correlators onto those of the magnetic limit.