Open Heterotic Strings

TL;DR

This work develops a topological classification of cosmic strings by externall observable charge, arguing that this charge governs absolute stability of long strings in string theory. It demonstrates that the SO(32) heterotic string can have endpoints in ten dimensions (and can be realized nonperturbatively via S-duality as a D1-brane ending on D9-branes), while the E8×E8 heterotic string cannot end in ten dimensions due to the structure of TrF^4; in four-dimensional compactifications, endpoint behavior becomes sensitive to the Euler characteristic χ and anomalous U(1) dynamics, enabling monopole-mediated endpoints for χ=2 and leading to AB or quasi-AB behavior for larger χ. The analysis combines anomaly cancellation, index theorems, and BF couplings to illuminate how boundary conditions at string endpoints reconcile with gauge invariance, with implications for nonperturbative heterotic physics and cosmology. Overall, the results support a stability conjecture for cosmic strings in string theory and highlight how compactification data governs whether heterotic strings can end.

Abstract

We classify potential cosmic strings according to the topological charge measurable outside the string core. We conjecture that in string theory it is this charge that governs the stability of long strings. This would imply that the SO(32) heterotic string can have endpoints, but not the E_8 x E_8 heterotic string. We give various arguments in support of this conclusion.