Degenerate, strong and stable Yang–Mills–Higgs pairs¶
Hu, Z., & Huang, P. (2017). Degenerate, strong and stable Yang–Mills–Higgs pairs. Journal of Geometry and Physics.
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Domain-specific¶
- Stable Yang–Mills–Higgs Pair
- “Strong” there imposes particular differential equations on a Hitchin pair; “stable” concerns a second-variation quadratic form along admitted deformations
This sourceTheir own terminology: ‘strong’ is defined by differential equations imposed on a Hitchin pair, ‘stable’ by the sign of a quadratic form obtained from the second variation along admitted deformations. Their setting: a Chern connection and Higgs field on a compact Kähler manifold, with the Yang–Mills–Higgs functional built from the curvature of the Hitchin–Simpson connection. Their Definition 3.3: a strong Yang–Mills–Higgs pair counts as stable when the Hermitian form from the second variation is positive on every admitted holomorphic deformation pair.
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- “Strong” there imposes particular differential equations on a Hitchin pair; “stable” concerns a second-variation quadratic form along admitted deformations
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