From vortices to instantons on the Euclidean Schwarzschild manifold
Abstract
The first irreducible solution of the $\SU (2)$ self-duality equations on the Euclidean
Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later
than the famous BPST instantons on $\rl^4$ were discovered. While soon after, in 1978,
the ADHM construction gave a complete description of the moduli spaces of instantons
on $\rl^4$, the case of the Euclidean Schwarzschild manifold has resisted many efforts
for the past 40 years. By exploring a correspondence between the planar Abelian vortices
and spherically symmetric instantons on ES, we obtain: a complete description of a
connected component of the moduli space of unit energy $\SU (2)$ instantons; new examples
of instantons with non-integer energy (and non-trivial holonomy at infinity); a complete
classification of finite energy, spherically symmetric, $\SU (2)$ instantons. As opposed
to the previously known solutions, the generic instanton coming from our construction
is not invariant under the full isometry group, in particular not static. Hence disproving
a conjecture of Tekin.
Type
Journal articlePermalink
https://hdl.handle.net/10161/16004Collections
More Info
Show full item recordScholars@Duke
Akos Nagy
William W. Elliott Assistant Research Professor
I work on elliptic geometric PDE's, mainly coming from low dimensional gauge theories
and mathematical physics.
This author no longer has a Scholars@Duke profile, so the information shown here reflects
their Duke status at the time this item was deposited.

Articles written by Duke faculty are made available through the campus open access policy. For more information see: Duke Open Access Policy
Rights for Collection: Scholarly Articles
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info