Factorisation of 3d N = 4 twisted indices and the geometry of vortex moduli space
Authors
Crew, Samuel
Dorey, Nick
Zhang, Daniel
Publication Date
2020-08-04Journal Title
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Volume
2020
Issue
8
Language
en
Type
Article
This Version
VoR
Metadata
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Crew, S., Dorey, N., & Zhang, D. (2020). Factorisation of 3d N = 4 twisted indices and the geometry of vortex moduli space. Journal of High Energy Physics, 2020 (8)https://doi.org/10.1007/jhep08(2020)015
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.
Keywords
Regular Article - Theoretical Physics, Supersymmetric Gauge Theory, Supersymmetry and Duality, Solitons Monopoles and Instantons, Differential and Algebraic Geometry
Identifiers
jhep08(2020)015, 13545
External DOI: https://doi.org/10.1007/jhep08(2020)015
This record's URL: https://www.repository.cam.ac.uk/handle/1810/308805