From vortices to instantons on the Euclidean Schwarzschild manifold
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.