Single-flavor Abelian mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$

Abstract

The supercoonformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ can be derived exactly by the localization technique and applied to the direct proof of Abelian mirror symmetry. We find two sets of parity conditions compatible with the unorientable property of ${\mathbb{RP}}^2$ and then rigorously show two kinds of Abelian mirror symmetry via the index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$.

6 pages, contribution to proceedings of IX International Symposium on Quantum Theory and Symmetries

References in corpus (4)

• Notes on SUSY Gauge Theories on Three-Sphere
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$