D-Branes and Physical States

TL;DR

This paper explores the cohomology classes of states associated with D-branes, revealing new off-shell structures and interactions between left and right movers that extend beyond on-shell descriptions.

Contribution

It introduces a general construction of off-shell cohomology classes for D-brane states, highlighting novel interactions and ghost dependencies at higher mass levels.

Findings

Off-shell cohomology differs from on-shell, with unique ghost structures.

Zero momentum cohomology forms multiplets of SO(D-1,1).

Higher mass level states show complex ghost interactions.

Abstract

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 more intricate ghost dependence.