KIAS-P12030 Quiver Invariants from Intrinsic Higgs States

In study of four-dimensional BPS states, quiver quantum mechanics plays a central role. The Coulomb phases capture the multi-centered nature of such states, and are well understood in the context of wall-crossing. The Higgs phases are given typically by F-term-induced complete intersections in the am-bient D-term-induced toric varieties, and the ground states can be far more nu-merous than the Coulomb phase counterparts. We observe that the Higgs phase BPS states are naturally and geometrically grouped into two parts, with one part given by the pulled-back cohomology from the D-term-induced ambient space. We propose that these pulled-back states are in one-to-one correspon-dence with the Coulomb phase states. This also leads us to conjecture that the index associated with the rest, intrinsic to the Higgs phase, is a fundamental invariant of quivers, independent of branches. For simple circular quivers, these intrinsic Higgs states belong to the middle cohomology and thus are all angular momentum singlets, supporting the single-center black hole interpretation