The Geometry of Calorons

Abstract

Calorons (periodic instantons) are anti-self-dual (ASD) connections on S^1 \times R^3 and form an intermediate case between instantons and monopoles. The ADHM and Nahm constructions of instantons and monopoles can be regarded as generalizations of a correspondence between ASD connections on the 4-torus, often referred to as the Nahm transform. This thesis describes how the Nahm transform can be extended to the case of calorons. It is shown how calorons can be constructed from Nahm data similar to that for monopoles, but defined over the circle. The inverse transformation, from the caloron to the Nahm data, is also described.

PhD Thesis, University of Edinburgh 2001, supervised by Michael Singer

References in corpus (1)

• Instantons, Monopoles and Toric HyperKaehler Manifolds

Cited by in corpus (8)

• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• A survey on Nahm transform
• A model for gauged skyrmions with low binding energies
• Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
• Symmetric calorons and the rotation map
• On the energy spectrum of Yang--Mills instantons over asymptotically locally flat spaces
• Spatially periodic instantons: Nahm transform and moduli
• From spatially periodic instantons to singular monopoles