T-branes, string junctions, and 6D SCFTs

Recent work on 6D superconformal field theories 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 multipronged strings stretched between stacks of intersecting 7-branes in F theory. These data let us determine the full structure of the nilpotent cone for each semisimple flavor symmetry algebra, and they further allow us to characterize symmetry-breaking patterns in quiverlike 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.