Boundary States for the Rolling D-branes in NS5 Background

In this paper we construct the time dependent boundary states describing the “rolling D-brane solutions” in the NS5 background discovered recently by Kutasov by means of the classical DBI analysis. We first survey some aspects of non-compact branes in the NS5 background based on known boundary states in the N = 2 Liouville theory. We consider two types of non-compact branes, one of which is BPS and the other is non-BPS but stable. Then we clarify how to Wick-rotate the non-BPS one appropriately. We show that the Wick-rotated boundary state realizes the correct trajectory of rolling D-brane in the classical limit, and leads to well behaved spectral densities of open strings due to the existence of non-trivial damping factors of energy. We further study the cylinder amplitudes and the emission rates of massive closed string modes.