Imaginary time D-branes to all orders

TL;DR

This paper develops a method to compute string amplitudes involving periodic arrays of D-branes in imaginary time, demonstrating their equivalence to pure closed string backgrounds through explicit calculations and theoretical arguments.

Contribution

It introduces a general prescription for all-order amplitude computations involving imaginary time D-branes, extending previous work and confirming their interpretation as pure closed string backgrounds.

Findings

Closed string amplitudes with b boundaries equal those with b insertions of a specific state

Explicit computation of the annulus amplitude supports the prescription

Higher order amplitudes are consistent with open and closed string field theory

Abstract

Extending the work of Gaiotto, Itzhaki and Rastelli in hep-th/0304192, we derive a general prescription for computing amplitudes involving a periodic array of D-branes in imaginary time to arbitrary order. We use this prescription to show that closed string amplitudes with b boundaries are identical to closed string amplitudes with b additional insertions of a particular physical closed string state. We perform an explicit computation for the annulus, and argue on the basis of open and closed string field theory for higher order amplitudes. We also discuss possible subtleties in the prescription related to collisions of boundaries and insertions, and argue that they are harmless. This verifies the proposal that a periodic array of D-branes in imaginary time corresponds to a pure closed string background.