Periodic Monopoles from Spectral Curves

Understand

We consider $\text{SU}(2)$ Bogomolny equations on $\mathbb{R}^2\times\hat{S}^1$ and use the spectral curve defined by the holonomy in the periodic direction to approximate the fields in the limit of large size to period ratio.

• Symmetries of the Nahm transform allow a study of the effective two dimensional dynamics, which is compared with known results on the full moduli space.
• The techniques are applied to systems of higher charge and higher rank gauge group, allowing a direct comparison to other periodic Yang-Mills systems.