Multi-boundary effects in Dirichlet String Theory

TL;DR

This paper investigates string amplitudes with Dirichlet boundaries, analyzing divergences and high-energy behavior, revealing divergence-free helicity amplitudes and power-law asymptotics in certain configurations.

Contribution

It provides a path integral analysis of Dirichlet boundary effects in string theory, identifying divergence-free amplitudes and their asymptotic behavior.

Findings

Certain helicity amplitudes are divergence-free to all orders

High energy amplitudes exhibit power-law behavior

Analysis clarifies boundary effects in string scattering

Abstract

String amplitudes with an arbitrary number of world-sheet boundaries on which the coordinates satisfy Dirichlet boundary conditions are analyzed in a path integral framework. Special attention is payed to the novel divergences associated with such conditions. Certain helicity amplitudes involving massless closed-string states are free of such divergences to all orders in perturbation theory and their behavior can be analysed unambiguously. The high energy fixed-angle behavior of these amplitudes is discussed in the presence of one or two boundaries and the asymptotic behavior of the amplitudes is shown to be power behaved.