Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes

TL;DR

This paper investigates the strongly coupled physics of non-Higgsable seven-branes in F-theory, revealing that order-one string coupling regions are common, and explores the related non-perturbative phenomena and BPS states.

Contribution

It introduces a novel analysis of strongly coupled regions in F-theory using elliptic functions, linking non-perturbative branes to weakly coupled counterparts and exploring their associated BPS states.

Findings

String coupling is order one near non-Higgsable seven-branes.

Non-perturbative $SU(3)$ and $SU(2)$ branes relate to weakly coupled D7-branes via Hanany-Witten moves.

D3-branes probe Argyres-Douglas theories near these branes.

Abstract

Geometrically non-Higgsable seven-branes carry gauge sectors that cannot be broken by complex structure deformation, and there is growing evidence that such configurations are typical in F-theory. We study strongly coupled physics associated with these branes. Axiodilaton profiles are computed using Ramanujan's theories of elliptic functions to alternative bases, showing explicitly that the string coupling is order one in the vicinity of the brane; that it sources nilpotent $SL(2,\mathbb{Z})$ monodromy and therefore the associated brane charges are modular; and that essentially all F-theory compactifications have regions with order one string coupling. It is shown that non-perturbative $SU(3)$ and $SU(2)$ seven-branes are related to weakly coupled counterparts with D7-branes via deformation-induced Hanany-Witten moves on $(p,q)$ string junctions that turn them into fundamental open strings; only the former may exist for generic complex structure. D3-brane near these and the Kodaira type II seven-branes probe Argyres-Douglas theories. The BPS states of slightly deformed theories are shown to be dyonic string junctions.