Hidden Selection Rules, M5-instantons and Fluxes in F-theory

TL;DR

This paper develops a new method to analyze how fluxed M5-instantons contribute to the F-theory effective action, revealing hidden selection rules and their relation to massive and massless U(1) symmetries, with implications for Yukawa couplings.

Contribution

It introduces a novel approach using homological relations to study fluxed M5-instantons and their role in generating charged matter F-terms in F-theory.

Findings

Fluxed M5-instantons detect geometrically massive U(1)s.

Non-generic embeddings can probe locally massless U(1)s.

Proposes new non-perturbative corrections to Yukawa couplings.

Abstract

We introduce a new approach to investigate the selection rules governing the contributions of fluxed M5-instantons to the F-theory four-dimensional effective action, with emphasis on the generation of charged matter F-terms. The structure of such couplings is unraveled by exploiting the perturbative and non-perturbative homological relations, introduced in our companion paper arXiv:1506.06764, which encode the interplay between the self-dual 3-form flux on the M5-brane, the background 4-form flux and certain fibral curves. The latter are wrapped by time-like M2-branes representing matter insertions in the instanton path integral. In particular, we clarify how fluxed M5-instantons detect the presence of geometrically massive $U(1)$s which are responsible for `hidden' selection rules. We discuss how for non-generic embeddings the M5-instanton can probe `locally massless' $U(1)$ symmetries if the rank of its Mordell-Weil group is enhanced compared to that of the bulk. As a phenomenological off-spring we propose a new type of non-perturbative corrections to Yukawa couplings which may change the rank of the Yukawa matrix. Along the way, we also gain new insights into the structure of massive $U(1)$ gauge fluxes in the stable degeneration limit.