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.

We investigate the giant gravitons in the maximally supersymmetric IIB ppwave from several viewpoints: (i) the dynamics of D3-branes, (ii) the world-sheet description and (iii) the correlation functions in the dual N=4 Yang-Mills theory. In particular, we derive the BPS equation of a D3-brane with magnetic flux, which is equivalent to multiple D-strings, and discuss the behavior of solutions in the presence of RR-flux. We find solutions which represent the excitations of the giant gravitons in that system.This result 8 shows that the single particle state of (2.9) is well defined (i.e. not mixed with multiparticle states) if we assume 9 J 2 /N ≫ 1. Thus the condition that the description of BPS operator (2.9) should describe the geometrical object of giant graviton requires at 5 The gauge dual of the latter type, which allows the exact world-sheet analysis, was discussed in[18] and the agreement of anomalous dimension of their fluctuations is verified (see also [34] for BPS fluctuations). 6 There are several results on the non-renormalization of extremal correlators e.g.[35] even for multitrace operators. Thus the results do not receive no g Y M corrections. We would like to thank S.Ramgoolam very much for this argument. 7 The two point function, which is used to normalize other correlation functions, is given by ŌThe exponential behaviour may suggest a sort of a tunneling effect. We would like to thank S.Minwalla very much for suggesting this point and also other several useful comments. 9 More precisely, here we mean that J 2 /N is always finite taking the limit N → ∞ and that the value J 2 /N is enough larger than one.10 The factor of sinh(J 2 /2N ) comes from the the two point function [38,39] TrZ J TrZ J = JN J sinh(J 2 /2N ), which is used to normalize. 11 The latter bound represents the critical point where gravitons become giant as discussed in [5].

We study rolling radion dynamics of electrified D-brane in NS5-brane background, both in effective field theory and in full open string theory. We construct exact boundary states and, from them, extract conserved Noether currents. We argue that T-duality and Lorentz boost offer an intuitive approach. In the limit of large number of NS5-branes, both boundary wave functions and conserved currents are sharply peaked and agree with those deduced from the effective field theory. As the number of NS5-branes is reduced, width around the peak becomes wider by string corrections. We also study radiative decay process. By applying Lorentz covariance, we show how the decay of electrified D-brane is related to that of bare D-brane. We compute spectral moments of final state energy and winding quantum number. Using Lorentz covariance argument, we explain in elementary way why winding quantum number should be included and derive rules how to do so. We conclude that Kutasov's "geometric realization" between radion rolling dynamics and tachyon rolling dynamics holds universally, both for bare and electrified D-branes.