Point-like Instantons and the Spin(32)/Z2 Heterotic String

TL;DR

This work analyzes heterotic strings with gauge group $Spin(32)/Z_2$ on K3 via F-theory, uncovering two point-like instanton types: the traditional simple instanton and a novel hidden obstructer tied to a generalized second Stiefel-Whitney class tilde w2. The study shows that four simple instantons coalescing at an orbifold point generate a massless tensor and provide a mechanism to interpolate to the hidden obstructer, while combinations of instantons yield large gauge groups up to rank 128 and many tensor multiplets. A detailed F-theory dual describes how simple instantons appear as lines of I2 fibers, how collisions induce sp(k) sectors and Sp(4) enhancements, and how massless tensors arise from Delta collisions; the work also connects to E8×E8 duals and GP models and demonstrates intricate phase transitions between tensor and hypermultiplet moduli. Overall, tilde w2 controls the global holonomy and the possible gauge content, and coalesced instantons illuminate a rich nonperturbative landscape of six-dimensional vacua with significant gauge-group diversity and tensor dynamics that are encoded geometrically in elliptic Calabi-Yau fibrations. The results illustrate a coherent picture where hidden obstructers and simple instantons are related through tensor moduli, enabling large, anomaly-free theories and providing a concrete geometric framework for understanding nonperturbative heterotic vacua.

Abstract

We consider heterotic string theories compactified on a K3 surface which lead to an unbroken perturbative gauge group of Spin(32)/Z2. All solutions obtained are combinations of two types of point-like instanton --- one ``simple type'' as discovered by Witten and a new type associated to the ``generalized second Stiefel-Whitney class'' as introduced by Berkooz et al. The new type of instanton is associated to an enhancement of the gauge symmetry by Sp(4) and the addition of a massless tensor supermultiplet. It is shown that if four simple instantons coalesce at an orbifold point in the K3 surface then a massless tensor field appears which may be used to interpolate between the two types of instanton. By allowing various combinations of point-like instantons to coalesce, large gauge groups (e.g., rank 128) with many massless tensor supermultiplets result. The analysis is done in terms of F-theory.

Figures (7)

• Figure 1: Lens space around an exceptional divisor.
• Figure 2: Blowing up the $\Delta"$ collision with $C_0$.
• Figure 3: F-theory picture of Gimon-Polchinski models.
• Figure 4: Four simple instantons collide with an orbifold point.
• Figure 5: $k$ simple instantons hitting a hidden obstructer.