Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of the $AH+2$ subfactor   We give two different proofs of the existence of the $AH+2$ subfactor, which
is a $3$-supertransitive self-dual subfactor with index $\frac{9+\sqrt{17}}{2}
$. The first proof is a direct construction using connections on graphs and
intertwiner calculus for bimodule categories. The second proof is indirect, and
deduces the existence of $AH+2$ from a recent alternative construction of the
Asaeda-Haagerup subfactor and fusion combinatorics of the Brauer-Picard
groupoid.

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The categories of this paper are: plasm-ph
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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: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn