Closed strings as imaginary D-branes

Abstract

Sen has recently drawn attention to an exact time-dependent Boundary Conformal Field Theory with the space-time interpretation of brane creation and annihilation. An interesting limit of this BCFT is formally equivalent to an array of D-branes located in imaginary time. This raises the question: what is the meaning of D-branes in imaginary time? The answer we propose is that D-branes in imaginary time define purely closed string backgrounds. In particular we prove that the disk scattering amplitude of m closed strings off an arbitrary configuration of imaginary branes is equivalent to a sphere amplitude with m + 1 closed string insertions. The extra puncture is a specific closed string state, generically normalizable, that depends on the details of the brane configuration. We study in some detail the special case of the array of imaginary D-branes related to Sen's BCFT and comment on its space-time interpretation. We point out that a certain limit of our set-up allows to study classical black hole creation and suggests a relation between Choptuik's critical behavior and a phase-transitionà la Gregory-Laflamme. We speculate that open string field theory on imaginary D-branes is dual to string theory on the corresponding closed string background.

D-brane decay in two-dimensional string theory

“…A more detailed study of Dp-brane decay was carried out in [6]- [24] and led to many new insights. A number of puzzles remain however; for example, to leading order in g s the number of closed string produced in D0-brane decay is UV divergent and one needs to go beyond tree level for handling this divergence.…”

Imaginary time D-branes to all orders

“…For more general brane configurations see Appendix A. The prescription of [1] is recovered by setting b = 1. …”

“…Boundary-boundary singularities will arise when there are more boundaries. As explained in [1], the poles coming from collisions of vertex operator insertions (4.6) are harmless, since one can always define the amplitude by analytically continuing the external momenta p i off-shell away from the singularity. The same argument does not work for the boundary momenta k j , since the amplitude contains an integral over all their possible values.…”

“…Recently, another type of open/closed string duality has been revealed. Gaiotto, Itzhaki and Rastelli have shown that closed string disk scattering amplitudes from a periodic array of D-branes in imaginary time are identical to purely closed string sphere amplitudes with an additional insertion of a particular physical closed string state [1]. This led to the proposal that an array of D-branes in imaginary time corresponds to a particular pure closed string background, and that perhaps any configuration of D-branes which are localized in imaginary (or complex) time corresponds to some pure closed string background.…”

“…It is therefore natural to expect that it can be described purely in terms of closed strings. The authors of [1] derived a prescription for computing disk amplitudes for Dbranes in imaginary time using a specific prescription for analytically continuing amplitudes for D-branes in real space. Applying this to the two-point (and more generally n-point) disk amplitude shows that the only contribution comes from the limit where the size of the boundary shrinks to a point, and that this corresponds to an additional insertion of a specific physical closed string state |W .…”