On Superstring Disk Amplitudes in a Rolling Tachyon Background

TL;DR

This paper extends the calculation of superstring disk amplitudes in a rolling tachyon background, expressing them as Toeplitz determinants and analyzing the emission of closed superstrings from a decaying non-BPS brane.

Contribution

It provides a novel analytical framework for superstring disk amplitudes in a rolling tachyon background, extending previous bosonic string results to superstrings.

Findings

Disk amplitudes expressed as Toeplitz determinants

Analytical results for bulk-boundary amplitudes

Average energy of emitted superstrings calculated

Abstract

We study the tree level scattering or emission of n closed superstrings from a decaying non-BPS brane in Type II superstring theory. We attempt to calculate generic n-point superstring disk amplitudes in the rolling tachyon background. We show that these can be written as infinite power series of Toeplitz determinants, related to expectation values of a periodic function in Circular Unitary Ensembles. Further analytical progress is possible in the special case of bulk-boundary disk amplitudes. These are interpreted as probability amplitudes for emission of a closed string with initial conditions perturbed by the addition of an open string vertex operator. This calculation has been performed previously in bosonic string theory, here we extend the analysis for superstrings. We obtain a result for the average energy of closed superstrings produced in the perturbed background.