Tunneling solutions in topological field theory on R x S-3 x I

Journal article, 2012

We consider a topologically twisted version, recently introduced by Witten, of five-dimensional maximally supersymmetric Yang-Mills theory on a five-manifold of the form M-5 = RxW(3)xI. If the length of the interval I is sufficiently large, the supersymmetric localization equations admit pairs of static solutions (with the factor R interpreted as Euclidean time). However, these solutions disappear for a sufficiently short I, so by the topological invariance of the theory, they must be connected by an interpolating dynamic instanton solution. We study this for the case that W-3 is a three-sphere S-3 with the standard metric by making a spherically symmetric Ansatz for all fields. The solution is given as a power series in a parameter related to the length of I, and we give explicit expressions for the first non-trivial terms.