Instantons and Killing spinors

Abstract

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

40 pages, 2 figures v2: author email addresses and affiliations added

References in corpus (10)

• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• The Srni lectures on non-integrable geometries with torsion
• Type IIA AdS4 compactifications on cosets, interpolations and domain walls
• Examples of Riemannian Manifolds with non-negative sectional curvature
• Gauge Theory in higher dimensions, II
• Instantons and Yang-Mills Flows on Coset Spaces
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Construction of Noncommutative Instantons in 4k Dimensions
• Homogeneous heterotic supergravity solutions with linear dilaton
• Hermitian Yang-Mills instantons on resolutions of Calabi-Yau cones

Cited by in corpus (44)

• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• M5-branes from gauge theories on the 5-sphere
• Supersymmetric Gauge Theories on the Five-Sphere
• Connections, Field Redefinitions and Heterotic Supergravity
• The infinitesimal moduli space of heterotic $G_2$ systems
• Instantons on Special Holonomy Manifolds
• Instantons on the exceptional holonomy manifolds of Bryant and Salamon
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• On twisted N=2 5D super Yang-Mills theory
• Moduli Spaces of Contact Instantons
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Indices for 6 dimensional superconformal field theories
• Deformations of nearly Kähler instantons
• Higher-degree Dirac Currents of Twistor and Killing Spinors in Supergravity Theories
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Gauge theory on Aloff-Wallach spaces
• Instantons on sine-cones over Sasakian manifolds
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Left-invariant Einstein metrics on $S^3\times S^3$
• Sasakian quiver gauge theories and instantons on the conifold
• Instantons on Calabi-Yau cones
• A method of deforming G-structures
• Instantons in six dimensions and twistors
• Moduli of $G_2$ structures and the Strominger system in dimension 7
• Instantons on the six-sphere and twistors
• Instantons on conical half-flat 6-manifolds
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Note on a Cohomological Theory of Contact-Instanton and Invariants of Contact Structures
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds
• The heterotic G${}_2$ system with reducible characteristic holonomy
• ${\mathrm{G}}_2$-instantons on the 7-sphere
• Instantons, five-branes and fractional strings
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Instantons on Calabi-Yau and hyper-Kähler cones
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint
• $\mathrm{Spin}(7)$-Instantons from evolution equations
• Families of solutions of the heterotic G${}_2$ system
• Instantons on Cylindrical Manifolds