On a hyperholomorphic line bundle over the Coulomb branch

Details On a hyperholomorphic line bundle over the Coulomb branch On a hyperholomorphic line bundle over the Coulomb branch

2011-10-07

arxiv.org/abs/1110.1619v1

Physics

High Energy Physics

High Energy Physics - Theory

27 pages

Scientific paper

Given an N=2 supersymmetric field theory in four dimensions, its dimensional reduction on S^1 is a sigma model with hyperkahler target space M. We describe a canonical line bundle V on M, equipped with a hyperholomorphic connection. The construction of this connection is similar to the known construction of the metric on M itself: one begins with a simple "semiflat" connection and then improves it by including contributions weighed by the degeneracies of BPS particles going around S^1. We conjecture that V describes the physics of the theory dimensionally reduced on NUT space.

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