Unitarity Meets Channel-Duality for Rolling / Decaying D-Branes

TL;DR

This paper examines the decay and rolling of D-branes, revealing overlooked contributions crucial for unitarity and channel duality, especially in the case of accelerated D-branes, through open string channel analysis.

Contribution

It provides an ab initio derivation highlighting previously neglected contributions to spectral amplitudes, ensuring unitarity and channel duality in D-brane dynamics.

Findings

Overlooked contributions are crucial for unitarity.

The contribution is absent in decay but present in rolling D-branes.

Ensures optical theorem at each string loop order.

Abstract

Investigations for decay of unstable D-brane and rolling of accelerated D-brane dynamics have revealed that various proposed prescriptions give different result for spectral amplitudes and observables. Here, we study them with particular attention to unitarity and open-closed channel duality. From "ab initio" derivation in the open string channel, both in Euclidean and Lorentzian worldsheet approaches, we find heretofore overlooked contribution to the spectral amplitudes and obervables. The contribution is fortuitously absent for decay of unstable D-brane, but is present for rolling of accelerated D-brane. We finally show that the contribution is imperative for ensuring unitarity and optical theorem at each order in string loop expansion.