Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds

Abstract

In four dimensions, 't Hooft symbols offer a compact and powerful framework for describing the self-dual structures fundamental to instanton physics. Extending this to six dimensions, the six-dimensional 't Hooft symbols can be constructed using the isomorphism between the Lorentz group $Spin(6)$ and the unitary group $SU(4)$. We demonstrate that the six-dimensional self-dual structures governed by the Hermitian Yang-Mills equations can be elegantly organized using these generalized 't Hooft symbols. We also present a systematic method for constructing Hermitian Yang-Mills instantons from spin connections on six-dimensional manifolds using the generalized 't Hooft symbols. We provide a thorough analysis of the topological invariants such as instanton and Euler numbers.

35 pages, no figure; to be published in JHEP

References in corpus (10)

• The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets
• New string vacua from twistor spaces
• Dimensional Reduction of the Heterotic String over nearly-Kaehler manifolds
• Yang-Mills Instantons from Gravitational Instantons
• Instantons and Yang-Mills Flows on Coset Spaces
• Yang-Mills Instantons and Dyons on Group Manifolds
• Algebraic Properties of Riemannian Manifolds
• Anatomy of Einstein Manifolds
• Dynamical Compactification with Matter
• Generalization of Instanton-Induced Inflation and Dynamical Compactification