A new kind of McKay correspondence from non-Abelian gauge theories

Abstract

The boundary chiral ring of a 2d gauged linear sigma model on a Kähler 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 $D^{♭}(X)$. 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.

arXiv comment29 pages, harvmac(b), 2 figs

References in corpus (13)

• Phases of $N=2$ Theories In Two Dimensions
• D-Branes And K-Theory
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• D-Branes And Mirror Symmetry
• Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• D-branes and Discrete Torsion II
• Phases of Supersymmetric D-branes on Kaehler Manifolds and the McKay correspondence
• Chern-Simons Gauge Theory As A String Theory
• Linear Models of Supersymmetric D-Branes
• D-branes on Stringy Calabi-Yau Manifolds
• D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
• Boundary Rings and N=2 Coset Models

Cited by in corpus (11)

• Symmetries of Toric Duality
• Derived Categories and Zero-Brane Stability
• D-Brane Stability and Monodromy
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• Enhanced D-Brane Categories from String Field Theory
• Quantum periods of Calabi-Yau fourfolds
• On Decay of K-theory
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Boundary Rings and N=2 Coset Models
• Closed String Tachyons, Non-Supersymmetric Orbifolds and Generalised McKay Correspondence
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories