Generalized quiver mutations and single-centered indices

Abstract

Quiver quantum mechanics is invariant under Seiberg duality. A mathematical consequence is that the cohomology of the Higgs branch moduli space is invariant under mutations of the quiver. The Coulomb branch formula, on the other hand, conjecturally expresses the Poincaré / Dolbeault polynomial of the Higgs branch moduli space in terms of certain quantities known as single-centered indices. In this work we determine the transformations of these single-centered indices under mutations. Moreover, we generalize these mutations to quivers whose nodes carry single-centered indices different from unity. Although the Higgs branch description of these generalized quivers is currently unknown, the Coulomb branch formula is conjectured to be invariant under generalized mutations.

33 pages, 1 figure; a mathematica notebook using an updated version of the CoulombHiggs.m package released along with our previous work arXiv:1302.5498 is included as ancillary file; v2: refs added, one extra paragraph in sec 2.2

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Cited by in corpus (9)

• Vafa-Witten invariants from exceptional collections
• The Coulomb Branch Formula for Quiver Moduli Spaces
• Abelianization of BPS Quivers and the Refined Higgs Index
• Quiver indices and Abelianization from Jeffrey-Kirwan residues
• Quivers, Line Defects and Framed BPS Invariants
• Remarks on 2d Unframed Quiver Gauge Theories
• Pure-Higgs states from the Lefschetz-Sommese theorem
• Attractor invariants, brane tilings and crystals
• Elliptic genera from multi-centers