# T-Branes at the Limits of Geometry

## TL;DR

This paper explores the geometric limits of T-branes in 6D F-theory compactifications, focusing on irregular poles in Hitchin systems and their role in engineering wild Higgs bundles within a unified framework.

## Contribution

It introduces a geometric formulation that unifies various wild Hitchin systems by tuning gauge singlet moduli, revealing new mechanisms for engineering complex Higgs bundles.

## Key findings

- Wild Higgs bundles can be engineered via irregular poles in Hitchin systems.
- Multiple matter fields at the same point lead to higher-order poles.
- Physical constraints limit the order of irregular poles.

## Abstract

Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is a Hitchin-like system in which simple and irregular poles emerge at marked points of the geometry. When multiple matter fields localize at the same point in the geometry, the associated Higgs field can exhibit irregular behavior, namely poles of order greater than one. This provides a geometric mechanism to engineer wild Higgs bundles. Physical constraints such as anomaly cancellation and consistent coupling to gravity also limit the order of such poles. Using this geometric formulation, we unify seemingly different wild Hitchin systems in a single framework in which orders of poles become adjustable parameters dictated by tuning gauge singlet moduli of the F-theory model.