Closed strings as imaginary D-branes

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-transition à 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.