Dirichlet Strings

TL;DR

This paper studies Dirichlet boundary strings, deriving Green functions and analyzing their physical properties, revealing differences from traditional string theory in scattering amplitudes and high-energy behavior.

Contribution

It introduces a simple, general method for analyzing Dirichlet boundary strings and explores their spectral and scattering properties, differing from prior models.

Findings

Critical dimension remains 26 for bosonic Dirichlet strings

Scattering amplitudes differ dramatically from usual string theory

High energy, fixed angle scattering exhibits power-like behavior

Abstract

Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general enough, with which basic problems can be easily addressed. The Green function on a surface with Dirichlet boundaries is obtained through the Neumann Green function on the same surface, by employing a simple approach to Dirichlet conditions. An easy consequence of the simple calculation of the Green function is that in the simplest model, namely the bosonic Dirichlet string, the critical dimension is still 26, and the tachyon is still present in the spectrum, while the scattering amplitudes differ dramatically from those in the usual string theory. We discuss the high energy, fixed angle behavior of the four point scattering amplitudes on the disk and the annulus. We argue for general power-like behavior of arbitrary high energy, fixed angle scattering amplitudes. We also discuss the high temperature property of the finite temperature partition function on an arbitrary surface, and give an explicit formula of the one on the annulus.