Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Index theorem on $T^2/\mathbb{Z}_N$ orbifolds   We investigate chiral zero modes and winding numbers at fixed points on
$T^2/\mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem
for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, where
$n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$ are the
sums of the winding numbers at the fixed points on $T^2/\mathbb{Z}_N$. This
formula is complementary to our zero-mode counting formula on the magnetized
orbifolds with non-zero flux background $M \neq 0$, consistently with
substituting $M = 0$ for the counting formula $n_+ - n_- = (2M - V_+ +
V_-)/2N$.

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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg