Varieties of Abelian mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$

Abstract

We study 3d mirror symmetry with loop operators, Wilson loop and Vortex loop, and multi-flavor mirror symmetry through utilizing the ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ 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 SL$(2,\mathbb{Z})$ 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.

24 pages; v2: reference added; v3: formulas modified, comments added, a reference added, and published in JHEP

References in corpus (2)

• Superconformal indices of three-dimensional theories related by mirror symmetry
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$

Cited by in corpus (1)

• Pentagon identities arising in supersymmetric gauge theory computations