Point-like Instantons on K3 Orbifolds

TL;DR

The paper develops a precise geometric framework for understanding nonperturbative gauge enhancements arising from point-like instantons on K3 orbifolds by employing stable degenerations that connect heterotic string data to F-theory on elliptically fibreed Calabi–Yau threefolds. It analyzes both E8×E8 and Spin(32)/Z2 heterotic strings, deriving how instanton coalescence at ADE singularities generates local gauge algebras and extra tensor multiplets, with detailed results for J-invariant sectors and various quotient singularities. A key result is that stable degenerations neatly separate K3 moduli from vector-bundle moduli, enabling explicit mappings between heterotic moduli and F-theory geometry, and revealing deep connections (via birational equivalence) between the E8 and Spin(32)/Z2 descriptions on circle compactification. The work provides comprehensive tables and constructions for the local gauge algebras produced by k instantons on different singularities, and discusses the global implications for 6D theories, including potential maximal gauge content and the role of Mordell–Weil U(1) factors.

Abstract

The map between the moduli space of F-theory (or type II string) compactifications and heterotic string compactifications can be considerably simplified by using "stable degenerations". We discuss how this method applies to both the E8 x E8 and the Spin(32)/Z2 heterotic string. As a simple application of this method we derive some basic properties of the nonperturbative physics of collections of E8 or Spin(32)/Z2 point-like instantons sitting at A-D-E singularities on a K3 surface.

Figures (8)

• Figure 1: The stable degeneration.
• Figure 2: Point-like $E_8$ instantons in the simplest case.
• Figure 3: The stable degeneration of point-like $E_8$ instantons.
• Figure 4: 10 instantons on an $\mathsf{E}_8$ singularity.
• Figure 5: 11 instantons on an $\mathsf{E}_8$ singularity.