Abelianization of BPS quivers and the refined Higgs index

作者：Lee Seung Joo^*; Wang Zhao Long; Yi Piljin

来源：The Journal of High Energy Physics, 2014, 2014(2): 047.

DOI：10.1007/JHEP02(2014)047

• Black Holes in String Theory
• Extended Supersymmetry
• D-branes
• Differential and Algebraic Geometry

We count Higgs "phase" BPS states of general non-Abelian quiver, possibly with loops, by mapping the problem to its Abelian, or toric, counterpart and imposingWeyl invariance later. Precise Higgs index computation is particularly important for quivers with superpotentials; the Coulomb "phase" index is recently shown to miss important BPS states, dubbed intrinsic Higgs states or quiver invariants. We demonstrate how the refined Higgs index is naturally decomposed to a sum over partitions of the charge. We conjecture, and show in simple cases, that this decomposition expresses the Higgs index as a sum over a set of partition-induced Abelian quivers of the same total charge but generically of smaller rank. Unlike the previous approach inspired by a similar decomposition of the Coulomb index, our formulae compute the quiver invariants directly, and thus offer a self-complete routine for counting BPS states.

• 出版日期2014-2-11
• 单位西北大学