# T-Branes, String Junctions, and 6D SCFTs

## TL;DR

This paper links string junctions in F-theory to Higgs branch deformations in 6D SCFTs, providing a combinatorial approach to understanding symmetry breaking and nilpotent cones in these theories.

## Contribution

It introduces a combinatorial framework based on multi-pronged strings for analyzing Higgs deformations and symmetry breaking in 6D SCFTs from string theory.

## Key findings

- Determines the full structure of the nilpotent cone for flavor symmetries.
- Characterizes symmetry breaking patterns in quiver theories.
- Extends analysis to short quivers with correlated breaking patterns.

## Abstract

Recent work on 6D superconformal field theories (SCFTs) has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we return to the stringy origin of these theories and show that many aspects of these deformations can be understood in terms of simple combinatorial data associated with multi-pronged strings stretched between stacks of intersecting 7-branes in F-theory. This data lets us determine the full structure of the nilpotent cone for each semi-simple flavor symmetry algebra, and it further allows us to characterize symmetry breaking patterns in quiver-like theories with classical gauge groups. An especially helpful feature of this analysis is that it extends to "short quivers" in which the breaking patterns from different flavor symmetry factors are correlated.