Fractional branes and boundary states in orbifold theories

1999/06/30 by Duiliu-Emanuel Diaconescu, Jaume Gomis · 10 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane cosmology #Cohomology #Equivariant cohomology #Gravitational singularity #Holomorphic function #Mathematical physics #Mathematics #Mirror symmetry #Moduli space #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Orbifold #Physics #Pure mathematics #Quantum cohomology #Quantum mechanics #String theory #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1126-6708/2000/10/001

published as JHEP 0010 (2000) 001 · 48 pages, Harvmac, 3 postscript figures, references and a note added

arxiv created 1999/09/21 · openalex publication_date 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the D-brane spectrum of N=2 string orbifold theories using the boundary state formalism. The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion. Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not. This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology. We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space. The example C³/Z₃ is worked out in full detail using local mirror symmetry techniques. We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional P² cycle.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• A correspondence dual to McKay's
• Local Mirror Symmetry at Higher Genus
• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• Considerations of one-modulus Calabi-Yau compactifications: Picard-Fuchs equations, Kähler potentials and mirror maps
• Dirichlet Branes and Ramond-Ramond Charges
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
• Mtheory as a matrix model: A conjecture
• D-branes, Quivers, and ALE Instantons
• McKay correspondence

Cited by

• A Note onc= 1 Virasoro Boundary States and Asymmetric Shift Orbifolds
• BPS branes in discrete torsion orbifolds
• The U-plane of rank-one 4d N=2 KK theories
• Twisted boundary states in Kazama–Suzuki models
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local ℂℙ² C P 2
• Seiberg Duality is an Exceptional Mutation
• D-Branes, Pi-Stability and Theta-Stability
• D3/D7 branes at singularities: constraints from global embedding and moduli stabilisation
• D-brane stability and monodromy
• Landau–Ginzburg description of D-branes on ALE spaces