Instantons on Gravitons
arXiv:1007.0044 · doi:10.1007/s00220-011-1293-y
Abstract
Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. For a judiciously chosen bow the Nahm transform maps any bow solution to an instanton on an ALF space. We demonstrate that this map respects all complex structures on the moduli spaces, so it is likely to be an isometry, and use this fact to study the asymptotics of the moduli spaces of instantons on ALF spaces.
42 pages, 8 figures
References in corpus (28)
- Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
- Periodic Instantons with non-trivial Holonomy
- SU(2) Calorons and Magnetic Monopoles
- Gauge Fields and D-branes
- Aspects of Type IIB Theory on ALE Spaces
- D-branes, Monopoles and Nahm Equations
- Exact T-duality between Calorons and Taub-NUT spaces
- Sigma Models And The ADHM Construction Of Instantons
- Four-Dimensional Avatars of Two-Dimensional RCFT
- Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
- HyperKähler Quotient Construction of BPS Monopole Moduli Spaces
- Branes, Instantons, And Taub-NUT Spaces
- Gravitational Instantons of Type D_k
- Explicit Construction of Yang-Mills Instantons on ALE Spaces
- Singular Monopoles and Gravitational Instantons
- Moduli Spaces of Instantons on the Taub-NUT Space
- Quiver Varieties and Branching
- A hyperkahler structure on the cotangent bundle of a complex Lie group
- On Yang--Mills instantons over multi-centered gravitational instantons
- Asymptotic metrics for SU(N)-monopoles with maximal symmetry breaking
- Pursuing the double affine Grassmannian I: transversal slices via instantons on A_k-singularities
- Instantons and affine Lie algebras
- Monopoles and the Gibbons-Manton metric
- Geometric construction of new Yang-Mills instantons over Taub-NUT space
- New Instanton Solutions at Finite Temperature
- Harmonic functions and instanton moduli spaces on the multi-Taub--NUT space
- On some asymptotically flat manifolds with non maximal volume growth
- Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}
Cited by in corpus (33)
- Curvature, Cones, and Characteristic Numbers
- Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds
- Gravitational instantons with faster than quadratic curvature decay (II)
- Parameter counting for singular monopoles on R^3
- Moduli of Monopole Walls and Amoebas
- Semiclassical framed BPS states
- Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
- Yang-Mills Instantons from Gravitational Instantons
- On 6d N=(2,0) theory compactified on a Riemann surface with finite area
- On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
- Super Yang-Mills Theory with Impurity Walls and Instanton Moduli Spaces
- Monopole Bubbling via String Theory
- Singular Monopoles from Cheshire Bows
- Playing with the index of M-theory
- New quiver-like varieties and Lie superalgebras
- Characters of tangent spaces at torus fixed points and -mirror symmetry
- Bow varieties---geometry, combinatorics, characteristic classes
- Dynamics of monopole walls
- One Monopole with k Singularities
- Skyrmions from gravitational instantons
- Instantons on the Taub-NUT Space
- Wall Crossing from Dirac Zeromodes
- Spatially periodic instantons: Nahm transform and moduli
- On the energy spectrum of Yang--Mills instantons over asymptotically locally flat spaces
- Hyperkahler Metrics from Monopole Walls
- Line Operators in 4d Chern-Simons Theory and Cherkis Bows
- Instantons on multi-Taub-NUT Spaces II: Bow Construction
- Instantons and Bows for the Classical Groups
- Mukai duality on K3 surfaces from the differential geometric perspective
- Hyperspherical equivariant slices and basic classical Lie superalgebras
- A Compact Expression for Periodic Instantons
- Simulating Magnetic Monopole-Defect Dynamics
- An Application of the Index Theorem for Manifolds with Fibered Boundaries