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

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

2011-12-13

arxiv.org/abs/1112.2866v2

Physics

High Energy Physics

High Energy Physics - Theory

Added paragraph on instanton number

Scientific paper

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 =R x W_3 x I. 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.

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