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Factorisation of 3d N = 4 twisted indices and the geometry of vortex moduli space

Published version
Peer-reviewed

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Authors

Crew, Samuel 
Dorey, Nick 
Zhang, Daniel 

Abstract

Abstract: We study the twisted indices of N = 4 supersymmetric gauge theories in three dimensions on spatial S2 with an angular momentum refinement. We demonstrate factorisation of the index into holomorphic blocks for the T[SU(N)] theory in the presence of generic fluxes and fugacities. We also investigate the relation between the twisted index, Hilbert series and the moduli space of vortices. In particular, we show that each holomorphic block coincides with a generating function for the χt genera of the moduli spaces of “local” vortices. The twisted index itself coincides with a corresponding generating function for the χt genera of moduli spaces of “global” vortices in agreement with a proposal of Bullimore et al. We generalise this geometric interpretation of the twisted index to include fluxes and Chern-Simons levels. For the T[SU(N)] theory, the relevant moduli spaces are the local and global versions of Laumon space respectively and we demonstrate the proposed agreements explicitly using results from the mathematical literature. Finally, we exhibit a precise relation between the Coulomb branch Hilbert series and the Poincaré polynomials of the corresponding vortex moduli spaces.

Description

Keywords

Regular Article - Theoretical Physics, Supersymmetric Gauge Theory, Supersymmetry and Duality, Solitons Monopoles and Instantons, Differential and Algebraic Geometry

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1029-8479

Volume Title

2020

Publisher

Springer Berlin Heidelberg