  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.
