Taxonomy of Instanton Corrections in Infinite Distance Limits

TL;DR

This paper analyzes instanton corrections in infinite distance limits using a solvable example, identifying which instantons are generated by a one-loop Schwinger integral over light states, and classifying them within a taxonomy.

Contribution

It introduces a precise criterion for instanton generation via Schwinger integrals and classifies instantons in infinite distance limits using a taxonomy framework.

Findings

Schwinger integral captures instantons with actions in a specific parametric window.

The proposal is supported by analysis of toroidal compactifications in 8 and 7 dimensions.

The taxonomy classification determines the emergent instantonic spectrum in infinite distance limits.

Abstract

Using the BPS-protected higher derivative $R^4$-term as an exactly solvable example, we analyze which instanton corrections are generated by a one-loop Schwinger integral over the light towers of states that arise in infinite distance limits in moduli space. We find that the Schwinger integral fully captures precisely those instantons whose action lies parametrically in the window $(\Lambda_{\rm sp}/M_{\rm light})^{-1}\le {\rm S}_{\rm inst}\le \Lambda_{\rm sp}/M_{\rm light}$, that is, instantons whose action is bounded by the ratio of the gravity cutoff and the mass scale of the lightest tower. This proposal is supported by considering the entire moduli space of toroidal compactifications in eight dimensions, together with a number of limits in seven dimensions. In each case, integrating out the light towers via the Schwinger integral reproduces the complete contribution of the instantons within the above window. We further recast the proposal in terms of the taxonomy classification, allowing us to determine the emergent instantonic spectrum associated with any infinite distance limit.