Abstract
We study 3d mirror symmetry with loop operators, Wilson loop and Vortex loop, and multi-flavor mirror symmetry through utilizing the \( \mathrm{\mathbb{R}}{\mathrm{\mathbb{P}}}^2\times {\mathbb{S}}^1 \) index formula. The key identity which makes the above description work well is the mod 2 version of the Fourier analysis, and we study such structure, the S-operation in the context of a \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) \) action on 3d SCFTs. We observed that two types of the parity conditions basically associated with gauge symmetries which we call \( \mathcal{P} \)-type and \( \mathcal{C}\mathcal{P} \)-type are interchanged under mirror symmetry. We will also comment on the T-operation.
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ArXiv ePrint: 1512.02835
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Mori, H., Tanaka, A. Varieties of Abelian mirror symmetry on \( \mathrm{\mathbb{R}}{\mathrm{\mathbb{P}}}^2\times {\mathbb{S}}^1 \) . J. High Energ. Phys. 2016, 88 (2016). https://doi.org/10.1007/JHEP02(2016)088
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DOI: https://doi.org/10.1007/JHEP02(2016)088