Semiclassical Limits of Higgs Bundles and Hyperpolygon Spaces
Analysis
This paper explores the relationship between the Hitchin metric on the moduli space of strongly parabolic Higgs bundles and the hyperkähler metric on hyperpolygon spaces. It investigates the degeneration of the Hitchin metric as parabolic weights approach zero, showing that hyperpolygon spaces emerge as a limiting model. The work provides insights into the semiclassical behavior of the Hitchin metric and offers a finite-dimensional model for the degeneration of an infinite-dimensional hyperkähler reduction. The explicit expression of higher-order corrections is a significant contribution.
Key Takeaways
- •Investigates the degeneration of the Hitchin metric.
- •Hyperpolygon spaces serve as a limiting model.
- •Provides a finite-dimensional model for an infinite-dimensional reduction.
- •Higher-order corrections of the Hitchin metric are expressed explicitly.
Reference
“The rescaled Hitchin metric converges, in the semiclassical limit, to the hyperkähler metric on the hyperpolygon space.”