Dirichlet Strings

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.

25 pages, BROWN-HET-915, harvmac More discussion is added to section 3

References in corpus (2)

• Temperature Dependence of String Theory in the Presence of World-Sheet Boundaries
• Point-Like Interactions in String Theory Induced by 2-D Topological Gravity

Cited by in corpus (8)

• Combinatorics of Boundaries in String Theory
• Scattering of Strings from D-branes
• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
• Wilson Loops, Winding modes, and Domain Walls in Finite Temperature QCD
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Multi-boundary effects in Dirichlet String Theory
• D-Branes in Topological Membranes