Boundary State from Ellwood Invariants

Boundary states are given by appropriate linear combinations of Ishibashi states. Starting from any OSFT solution and assuming Ellwood conjecture we show that every coefficient of such a linear combination is given by an Ellwood invariant, computed in a slightly modified theory where it does not trivially vanish by the on-shell condition. Unlike the previous construction of Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is manifestly gauge invariant and it is also suitable for solutions known only numerically. The correct boundary state is readily reproduced in the case of known analytic solutions and, as an example, we compute the energy momentum tensor of the rolling tachyon from the generalized invariants of the corresponding solution. We also compute the energy density profile of Siegel-gauge multiple lump solutions and show that, as the level increases, it correctly approaches a sum of delta functions. This provides a gauge invariant way of computing the separations between the lower dimensional D-branes.