# From vortices to instantons on the Euclidean Schwarzschild manifold

Journal Article

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.

### Cited Authors

• Nagy, Á; Oliveira, G