String Scattering from Decaying Branes

TL;DR

This paper develops a well-defined formalism for string scattering from decaying D-branes, providing exact amplitude formulas, analyzing emission effects, and connecting to random matrix models and free fermion systems.

Contribution

It introduces an alternative, rigorous approach to compute string scattering amplitudes from decaying D-branes, avoiding unjustified analytic continuations and linking to advanced mathematical frameworks.

Findings

Exact closed-form amplitude expressions using Selberg integrals.

Perturbations can suppress or enhance high-energy closed string emission.

Large N limit theorems approximate the full scattering results.

Abstract

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szego, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.