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Description

The bosonic ghost algebra \beta\gamma appears in 3 dimensional N=4 QFTs via the work of Dimofte-Garner-Geracie-Hilburn, as well as Costello-Creutzig-Gaiotto. The category of modules of this VOA is the category of line operators of certain 3d N=4 theory. A small category of modules was studied by Ridout-Wood, and fusion structure is derived using free-field realizations. However, their category is too small to produce the correct algebra of bulk local operators. We study an enlarged category that does produce the correct bulk local operator algebra, and we showed that this category is equivalent to a category of modules of an affine lie super-algebra. This equivalence is an example of 3d mirror symmetry. We use this equivalence to compute fusion rules for indecomposable modules. This is a joint work with Andrew Ballin.