(1,0) gauge theories on the six-sphere
arXiv:1809.06272 · doi:10.21468/SciPostPhys.6.1.002
Abstract
We construct gauge theories with a vector-multiplet and hypermultiplets of supersymmetry on the six-sphere. The gauge coupling on the sphere depends on the polar angle. This has a natural explanation in terms of the tensor branch of theories on the six-sphere. For the vector-multiplet we give an off-shell formulation for all supersymmetries. For hypermultiplets we give an off-shell formulation for one supersymmetry. We show that the path integral for the vector-multiplet localizes to solutions of the Hermitian-Yang-Mills equation, which is a generalization of the (anti-)self duality condition to higher dimensions. For the hypermultiplet, the path integral localizes to configurations where the field strengths of two complex scalars are related by an almost complex structure.
arXiv comment33 pages, two appendices. v3: more typos fixed, a reference added, a field redefinition that makes the vector-multiplet action manifestly regular is discussed
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