Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconformal index on $\mathbb{RP}^2 \times \mathbb{S}^1$ and mirror
  symmetry   We study $\mathcal{N} = 2$ supersymmetric gauge theories on $\mathbb{RP}^2
\times \mathbb{S}^1$ and compute the superconformal index by using the
localization technique. We consider not only the round real projective plane
$\mathbb{RP}^2$ but also the squashed real projective plane $\mathbb{RP}^2_b$
which turns back to $\mathbb{RP}^2$ by taking a squashing parameter $b$ as $1$.
In addition, we found that the result is independent of the squashing parameter
$b$. We apply our new superconformal index to the check of the simplest 3d
mirror symmetry, i.e. the equivalence between the $\mathcal{N}=2$ SQED and the
XYZ model on $\mathbb{RP}^2 \times \mathbb{S}^1$. We prove it by using a
mathematical formula called the $q$-binomial theorem. We comment on the
$\mathcal{N}=4$ version of mirror symmetry, mirror symmetry via generalized
indices, and possibilities of generalizations from mathematical viewpoints.

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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org