Three looks at instantons in F-theory — New insights from anomaly inflow, string junctions and heterotic duality

Abstract

We discuss the physics of zero modes of ED3/M5 instantons at strong coupling from three different viewpoints. Motivated by an anomaly inflow argument, we give a prescription for describing neutral instanton modes in terms of string junctions, unifying the language with that used for charged modes. We proceed to discuss the physics of charged modes as we move between different points in the moduli space of F-theory compactified on K3. In particular, we show how, in going from the $E_6^3$ point to the SO(8)⁴ point, the structure of SO(8) zero modes arises from a non-trivial mixing of massless 27’s of E ₆ with massive modes stretching between different E ₆ stacks. We observe a similar mixing in going from SO(8)⁴ to $E_6^3$. Finally, we see how the zeroes of some exact worldsheet instanton superpotentials in heterotic backgrounds preserving E ₆ symmetry admit a physical interpretation in terms of low energy physics. We also discuss the behavior of the dual F-theory compactification as the superpotential approaches a zero. An interesting observation is that in the examples we study some of the zeroes of the superpotential correspond to points of E ₈ enhancement in the worldvolume of the dual M5 instanton, and more generally from enhancements of the singularity over the worldvolume of the instanton.