Combinatorics of Boundaries in String Theory

TL;DR

Polchinski investigates nonperturbative string effects as world-sheet boundaries, focusing on Dirichlet boundaries and showing their contributions are weighted by $e^{-O(1/g_{\rm st})}$. Through duality arguments and Fischler-Susskind cancellations, he demonstrates a consistent, boundary-driven mechanism that leaves perturbative closed-string physics intact while introducing controlled nonperturbative boundary effects. The work highlights a broader view where diverse boundary states govern nonperturbative phenomena, suggesting a unified, boundary-state framework beyond conventional perturbation theory. These insights illuminate the interplay between D-brane-like boundaries, world-sheet topology, and the cancellation of divergences in a nonperturbative regime, with potential implications for the broader landscape of string theories.

Abstract

We investigate the possibility that stringy nonperturbative effects appear as holes in the world-sheet. We focus on the case of Dirichlet string theory, which we argue should be formulated differently than in previous work, and we find that the effects of boundaries are naturally weighted by $e^{-O(1/g_{\rm st})}$.

Figures (2)

• Figure 1: a) Dirichlet disk amplitude with three closed-string vertex operators, with $V_1$ approaching the boundary. b) Conformally equivalent picture, two disks joined by a degenerating strip.
• Figure 2: a,b) Amplitudes which cancel the divergence and anomaly of figure 1. In each amplitude, there are three boundaries at a common position $X^\mu$.