Towards quantizing null p-branes: light-cone gauge analysis and physical Hilbert space

We study null p-branes, p-branes with a Carrollian p+1-dimensional worldvolume embedded in a generic D-dimensional flat Minkowski target space. This theory has a generalised BMS_p+1 gauge symmetry. By fixing the light-cone gauge, the BMS symmetry is partly fixed, leaving p “momentum constraints” alongside p-dimensional area-preserving diffeomorphisms. We quantise the theory in the light-cone gauge via canonical quantisation and construct the physical Hilbert space by imposing the remaining constraints using sandwich conditions: the constraints must vanish when sandwiched between any two physical states. We show that solutions to the sandwich conditions are classified into p + 1 distinct classes, which we completely specify. In addition, we discuss special and interesting case of membranes in four dimensions and examine the physical implications of the quantised null p-brane and its associated physical Hilbert space.