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Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery

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arxiv hep-th/0611346 v1 pith:2OQI7DRR submitted 2006-11-30 hep-th

Amihay Hanany , Christian Romelsberger This is my paper · ORCID
classification hep-th
keywords operatorsbranchescountinggaugeariseschiralfunctionsgenerating
verification ladder T0 review T1 audit T2 compute T3 formal
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This note is presenting the generating functions which count the BPS operators in the chiral ring of a N=2 quiver gauge theory that lives on N D3 branes probing an ALE singularity. The difficulty in this computation arises from the fact that this quiver gauge theory has a moduli space of vacua that splits into many branches -- the Higgs, the Coulomb and mixed branches. As a result there can be operators which explore those different branches and the counting gets complicated by having to deal with such operators while avoiding over or under counting. The solution to this problem turns out to be very elegant and is presented in this note. Some surprises with "surgery" of generating functions arises.

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Cited by 3 Pith papers

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  1. Abelian Orbifolds for Brane Brick Models

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.

  2. Quiver-Invariant Dualities between Brane Tilings

    hep-th 2026-01 conditional novelty 6.0 of 10

    A tilting mutation of brane tilings yields distinct superpotentials on the same quiver with identical mesonic moduli space, equivalent to a sequence of Seiberg dualities.

  3. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

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