Boundary conditions for GL-twisted N=4 SYM

Details Boundary conditions for GL-twisted N=4 SYM Boundary conditions for GL-twisted N=4 SYM

2011-06-20

arxiv.org/abs/1106.3845v2

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 1 figure, minor changes

Scientific paper

We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. We verify that each of these conditions defines a `middle-dimensional' subspace of the space of all bulk solutions. Taking the two boundaries of V into account should thus generically give a discrete set of solutions. We explicitly find the spherically symmetric solutions when W = S^3 endowed with the standard metric. For widely separated boundaries, these consist of a pair of solutions which coincide for a certain critical value of the boundary separation and disappear for even smaller separations.

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