Open Strings and Heterotic Instantons

TL;DR

This work argues that Shenker-type non-perturbative corrections in 10D heterotic strings originate from heterotic D-instantons, realized as disk diagrams with endpoints on a spacetime $(-1)$-brane and stabilized by an inflow of spacetime fermion zero modes. In the HO theory these effects are inherited from Type IIB via Hull's orientifold construction, with a tower of D-instantons descending to HO and wrapped HO D-strings contributing to $e^{-2\pi|n|/g_s}$-type terms; the instanton sector carries a nontrivial $\mathbb{Z}_2$ KO charge and is tied to the cobordism group $\Omega_{10}^{\mathrm{Spin}}(B\mathrm{SemiSpin}(32))\cong 10\mathbb{Z}_{2}$, implying a potential $(-1)$-form symmetry in the Swampland context. Green and Rudra’s results for the HO $R^{4}$ term, organized into a real-analytic Eisenstein series $E_{3/2}(i/g_s)$, support the D-instanton interpretation, with instanton sectors governed by $e^{-2\pi|n|/g_s}$; in HE, non-perturbative effects may arise from purely gravitational configurations or gauge-supported 0-branes in lower dimensions. The paper also discusses extensions to other heterotic theories and non-perturbative frameworks (e.g., matrix models), highlighting the need for a calculable open heterotic disk formalism and the broad implication that closed-string theories may require open-string sectors for completeness.

Abstract

Motivated by closed string perturbation theory arguments by S. Shenker, we consider non-perturbative effects of characteristic strength $\mathcal{O}(e^{-1/g_{s}})$, with $g_{s}$ the closed string coupling constant, in supersymmetric critical heterotic string theories. We argue that in 10D such effects arise from heterotic "D-instantons," i.e. heterotic disk diagrams, whose existence relies on a non-trivial interplay between worldsheet and spacetime degrees of freedom. In compactifications of the $\mathrm{SemiSpin}(32)$ heterotic string, we argue that similar effects can arise from wrapped Euclidean non-BPS "D-strings." Two general principles arise: The first is that the consistency of those heterotic branes on which the fundamental string can end relies on an inflow mechanism for spacetime degrees of freedom. The second is that Shenker's argument, taken to its logical conclusion, implies that all closed string theories must exhibit open strings as well.