Ákos Nagy, University of Waterloo and The Fields Institute
"Vortex-like instantons on the Euclidean Schwarzschild manifold"
By exploring a duality between planar Abelian vortices and SO(3) invariant SU(2) instantons in 4 dimensions, we construct new finite energy, irreducible solutions to the self-duality equations on the Euclidean Schwarzschild manifold. These solutions are not invariant under the action of the full isometry group, in particular they are not static. Thus, they provide counterexamples to a conjecture of Tekin on a possible, non-Abelian extension of Birkhoff's theorem in general relativity.
The main results include: A complete description of a connected component of the moduli space of unit charge instantons and new examples of instantons with non-integer energy, and non-trivial holonomy at infinity. The Uhlenbeck compactness of the corresponding moduli spaces is also understood.
This is a joint project with Gonçalo Oliveira (IMPA).
MC 5403