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.

arXiv comment35 pages, no figure; to be published in JHEP

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