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A new kind of McKay correspondence from non-Abelian gauge theories
High Energy Physics - Theory · Submitted 14 Mar 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We use this correspondence to elaborate on an extended notion of McKay correspondence that captures more general than orbifold singularities.
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The abstract, sentence by sentence
The boundary chiral ring of a 2d gauged linear sigma model on a K\"ahler manifold $X$ classifies the topological D-brane sectors and the massless open strings between them. While it is determined at small volume by simple group theory, its continuation to generic volume provides highly non-trivial information about the $D$-branes on $X$, related to the derived category $D^\flat(X)$. We use this correspondence to elaborate on an extended notion of McKay correspondence that captures more general than orbifold singularities. As an illustration, we work out this new notion of McKay correspondence for a class of non-compact Calabi-Yau singularities related to Grassmannians.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The boundary chiral ring of a 2d gauged linear sigma model on a K\"ahler manifold $X$ classifies the topological D-brane sectors and the massless open strings between them. | background 1.00 | 0.09 | 0.05 | asserted 1.00 |
| s1 | While it is determined at small volume by simple group theory, its continuation to generic volume provides highly non-trivial information about the $D$-branes on $X$, related to the derived category $D^\flat(X)$. | background 0.96 | 0.11 | 0.09 | asserted 1.00 |
| s2 | We use this correspondence to elaborate on an extended notion of McKay correspondence that captures more general than orbifold singularities. | contribution 0.98 | 0.88 | 0.49 | asserted 0.99 |
| s3 | As an illustration, we work out this new notion of McKay correspondence for a class of non-compact Calabi-Yau singularities related to Grassmannians. | contribution 0.88 | 0.94 | 0.17 | asserted 0.99 |
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The paper
Original abstract
The boundary chiral ring of a 2d gauged linear sigma model on a K\"ahler manifold $X$ classifies the topological D-brane sectors and the massless open strings between them. While it is determined at small volume by simple group theory, its continuation to generic volume provides highly non-trivial information about the $D$-branes on $X$, related to the derived category $D^\flat(X)$. We use this correspondence to elaborate on an extended notion of McKay correspondence that captures more general than orbifold singularities. As an illustration, we work out this new notion of McKay correspondence for a class of non-compact Calabi-Yau singularities related to Grassmannians.
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References
How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 2 papers
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GLSMs with nonabelian gauge symmetry have been studied in the literature, particularly in the context of understanding complete intersections in Grassmannians [ref] and in partial flag manifolds [ref] , and more recently in the context of understanding (skew-symmetric and symmetric) determinantal varieties [ref] .
Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties · Introduction and Summary of Results · 0.99
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This happens for instance for non-toric GIT quotients $Y$, which in the physics literature arise from two-dimensional $N=(2,2)$ non-Abelian gauged linear sigma models [ref] .
Quantum periods of Calabi-Yau fourfolds · Quantum cohomology of Calabi–Yau fourfolds · 0.84
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