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.
Highlights
One of the surprises from string theory is the prediction of whole new classes of quantum field theories decoupled from gravity
superconformal field theories (SCFTs) are generated by simultaneously contracting a configuration of curves in the base geometry
We primarily focus on 6D SCFTs generated by M5-branes probing an ADE singularity with flavor symmetry GADE × GADE, as well as tensor branch deformations of these cases to nonsimply laced flavor symmetry algebras
Summary
One of the surprises from string theory is the prediction of whole new classes of quantum field theories decoupled from gravity. The explicit characterization of nilpotent orbits in terms of string junctions allows us to study Higgs branch flows in which the number of gauge groups is small This case is especially interesting because there are nontrivial correlations on the symmetry-breaking patterns, one emanating from the left flavor symmetry G0 and the subsequent. This has been used to directly determine the Higgsed theory Even so, this derivation of the theory obtained after Higgsing involves a number of steps which are not entirely systematic, leading to potential ambiguities in cases where the number of gauge group factors in the quiver is sufficiently small that there is a nontrivial correlation in the symmetry-breaking pattern obtained from a pair of nilpotent orbits (one on the left and one on the right of the quiver). (2) Second, we determine how to consistently condense these multipronged string states to trigger brane recombination in the quiverlike gauge theory
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