1. Explicit construction of Hermitian Yang-Mills instantons on coset manifolds
- Author
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Jongmin Park and Hyun Seok Yang
- Subjects
Field Theories in Higher Dimensions ,Solitons Monopoles and Instantons ,Differential and Algebraic Geometry ,Nuclear and particle physics. Atomic energy. Radioactivity ,QC770-798 - Abstract
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.
- Published
- 2024
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