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arXiv · 2204.02997

Twisted Formalism for 3d $\mathcal{N}=4$ Theories

Niklas Garner
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Abstract

We describe the topological $A$ and $B$ twists of 3d $\mathcal{N}=4$ theories of hypermultiplets gauged by $\mathcal{N}=4$ vector multiplets as certain deformations of the holomorphic-topological ($HT$) twist of those theories, utilizing the twisted superfields of Aganagic-Costello-Vafa-McNamara describing $HT$-twisted 3d $\mathcal{N}=2$ theories. We rederive many known results from this perspective, including state spaces on Riemann surfaces, deformations induced by flavor symmetries, the boundary VOAs of Costello-Gaiotto, and the category of line operators as proposed by Costello-Dimofte-Gaiotto-Hilburn-Yoo. Along the way, we show how the secondary product of local operators in the holomorphic-topological twist is related to the secondary product in the fully topological twist.

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Niklas Garner. 2022-04-06. Twisted Formalism for 3d $\mathcal{N}=4$ Theories. https://arxiv.org/abs/2204.02997

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