Factorisation of 3d \(\mathcal{N} = 4\) twisted indices and the geometry of vortex moduli space
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Publication:2225691
DOI10.1007/JHEP08(2020)015zbMATH Open1454.81220arXiv2002.04573OpenAlexW3005939492MaRDI QIDQ2225691
Author name not available (Why is that?)
Publication date: 10 February 2021
Published in: (Search for Journal in Brave)
Abstract: We study the twisted indices of supersymmetric gauge theories in three dimensions on spatial with an angular momentum refinement. We demonstrate factorisation of the index into holomorphic blocks for the 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 genera of the moduli spaces of "local" vortices. The twisted index itself coincides with a corresponding generating function for the 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 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 Poincar'e polynomials of the corresponding vortex moduli spaces.
Full work available at URL: https://arxiv.org/abs/2002.04573
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