Boundaries & localisation with a topological twist
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Abstract We study the partition functions of topologically twisted 3d $$ \mathcal{N} $$ N = 2 gauge theories on a hemisphere spacetime with boundary HS2 × S1. We show that the partition function may be localised to either the Higgs branch or the Coulomb branch where the contributions to the path integral are vortex or monopole configurations respectively. Turning to $$ \mathcal{N} $$ N = 4 supersymmetry, we consider partition functions for exceptional Dirichlet boundary conditions that yield a complete set of ‘IR holomorphic blocks’. We demonstrate that these correspond to vertex functions: equivariant Euler characteristics of quasimap moduli spaces. In this context, we explore the geometric interpretation of both the Higgs and Coulomb branch localisation schemes in terms of the enumerative geometry of quasimaps and discuss the action of mirror symmetry.
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Acknowledgements: It is a pleasure to thank Mathew Bullimore, Adam Chalabi, Cyril Closset, Hunter Dinkins, Nick Dorey, Andrea Ferrari, Mark Gross, Nick Manton, Ivan Smith, Michael Walter, Claude Warnick, and Yutaka Yoshida for helpful discussions. SC and DZ are grateful to ICMAT for their hospitality while part of this work was completed. BZ is supported by a Trinity College internal graduate studentship. DZ is supported by a Junior Research Fellowship from St. John’s College, Oxford.
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1029-8479
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