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We define a class of space-times that we call asymptotically locallySchroedinger space-times. We consider these space-times in 3 dimensions, inwhich case they are also known as null warped AdS. The boundary conditions areformulated in terms of a specific frame field decomposition of the metric whichcontains two parts: an asymptotically locally AdS metric and a product of alightlike frame field with itself. Asymptotically we say that the lightlikeframe field is proportional to the particle number generator N regardless ofwhether N is an asymptotic Killing vector or not.  We consider 3-dimensional AlSch space-times that are solutions of the massivevector model. We show that there is no universal Fefferman-Graham (FG) typeexpansion for the most general solution to the equations of motion. We showthat this is intimately connected with the special role played by particlenumber. Fefferman-Graham type expansions are recovered if we supplement theequations of motion with suitably chosen constraints. We consider threeexamples. 1). The massive vector field is null everywhere. The solution in thiscase is exact as the FG series terminates and has N as a null Killing vector.2). N is a Killing vector (but not necessarily null). 3). N is null everywhere(but not necessarily Killing). The latter case contains the first examples ofsolutions that break particle number, either on the boundary directly or onlyin the bulk. Finally, we comment on the implications for the problem ofholographic renormalization for asymptotically locally Schroedingerspace-times.

Particle Number and 3D Schroedinger Holography