Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension Formulae and Generalised Deep Holes of the Leech Lattice
  Vertex Operator Algebra   We prove a dimension formula for the weight-1 subspace of a vertex operator
algebra $V^{\operatorname{orb}(g)}$ obtained by orbifolding a strongly
rational, holomorphic vertex operator algebra $V$ of central charge 24 with a
finite-order automorphism $g$. Based on an upper bound derived from this
formula we introduce the notion of a generalised deep hole in
$\operatorname{Aut}(V)$.
  Then we show that the orbifold construction defines a bijection between the
generalised deep holes of the Leech lattice vertex operator algebra $V_\Lambda$
with non-trivial fixed-point Lie subalgebra and the strongly rational,
holomorphic vertex operator algebras of central charge 24 with non-vanishing
weight-1 space. This provides the first uniform construction of these vertex
operator algebras and naturally generalises the correspondence between the deep
holes of the Leech lattice $\Lambda$ and the 23 Niemeier lattices with
non-vanishing root system found by Conway, Parker and Sloane.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph