No 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.

In a previous publication an exact expression was given for the Hartree potential in a perfect solid. The screening charge round a particular ion was expressed in terms of an effective dielectric tensor and here we examine the diagonal components of this tensor using a simple model of the electronic states in a semiconductor.