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AdS/CFT description of D-particle decay

O † ˆ OJ is shown to be inappropriate, even in the large-N limit. The reason is that the final state consists of a large number of particles. By computing all probabilities for finding multi-particle states in the coherent state, we deduce the bulk particle content of the final state of the sphaleron decay. The qualitative features of this spectrum are compared with the results expected from the gravity side, and agreement is found. The spectrum of type-IIB string theory contains, apart from the stable BPS and non-BPS states, also a wide variety of unstable D-branes. These unstable branes contain a tachyon field on their world-volume, and the condensation of this field corresponds to the decay of the brane. Recently, a lot of progress has been made in understanding the dynamical aspects of the decay of unstable branes. Most of the analysis was performed directly using boundary conformal field theory in flat space, initiated by Sen’s construction of the boundary states for decaying D-branes [1], or by using the c = 1 matrix model for the description of the decay of D-branes in 1+1 dimensional string theory [2]. In the present paper we would like to study the problem of decaying branes in the set-up of the “standard” AdS/CFT correspondence. As was argued by Harvey et al. [3], the unstable Dbranes in string-theory are equivalents of “sphalerons”: they are unstable solutions located at a saddle point of the potential in configuration space, at the top of a noncontractible loop [4]. In the context of the AdS/CFT conjecture, this correspondence between unstable D-branes and sphalerons is in fact even more direct. It has been argued by Drukker et al. [5] that the existence of sphaleronic saddle points in the potential of the theories on both sides is a feature which is preserved when going from weak to strong coupling, despite the fact that the precise form of the potential receives quantum corrections. The unstable D-particles of string theory are then in precise correspondence with known sphaleron solutions of the dual gauge theory. Kinematical aspects of this correspondence were investigated in detail in [5]. In the present paper, we will analyse dynamical aspects of this correspondence. Our analysis consists of three parts. First, we will construct the classical solution of the decaying sphaleron, and obtain a quantum