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Jan Manschot; Boris Pioline; Ashoke Sen
The Coulomb Branch Formula for Quiver Moduli Spaces
Confluentes Mathematici, 9 no. 2 (2017), p. 49-69, doi: 10.5802/cml.41
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Class. Math.: 16G20, 37P45, 81T60, 83E50
Keywords: representations of quivers, moduli spaces, quiver quantum mechanics, bound states

Résumé - Abstract

In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to ‘single-centered’ or ‘pure-Higgs’ states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the $\chi _{y}$-genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.

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