D-branes and physical states

States obtained by projecting boundary states, associated with D-branes, to fixed mass level and momentum generically define non-trivial cohomology classes. For on-shell states the cohomology is the standard one, but when the states are off shell the relevant cohomology is defined using a BRST operator with ghost zero-modes removed. The zero-momentum cohomology falls naturally into multiplets of SO(D - 1, 1). At the massless level, a simple set of D-brane configurations generates the full set of zero-momentum states of standard ghost number, including the discrete states. We give a general construction of off-shell cohomology classes, which exhibits a non-trivial interaction between left- and right-movers that is not seen in on-shell cohomology. This includes, at higher mass levels, states obtained from typical D-brane boundary states as well as states with a more intricate ghost dependence.