Closed Strings as Imaginary D-branes

TL;DR

This paper explores the concept of D-branes in imaginary time, showing they define purely closed string backgrounds and relate to phenomena like black hole creation and phase transitions.

Contribution

It proposes that imaginary time D-branes correspond to closed string backgrounds and establishes a link between boundary conformal field theory and closed string amplitudes.

Findings

Disk scattering amplitude with imaginary branes equals sphere amplitude with an extra insertion.

Special case relates to Sen's BCFT and its space-time interpretation.

Limit study suggests connections to black hole formation and phase transitions.

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-transition a` 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.