Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K3 Elliptic Genus and an Umbral Moonshine Module   Umbral moonshine connects the symmetry groups of the 23 Niemeier lattices
with 23 sets of distinguished mock modular forms. The 23 cases of umbral
moonshine have a uniform relation to symmetries of $K3$ string theories.
Moreover, a supersymmetric vertex operator algebra with Conway sporadic
symmetry also enjoys a close relation to the $K3$ elliptic genus. Inspired by
the above two relations between moonshine and $K3$ string theory, we construct
a chiral CFT by orbifolding the free theory of 24 chiral fermions and two pairs
of fermionic and bosonic ghosts. In this paper we mainly focus on the case of
umbral moonshine corresponding to the Niemeier lattice with root system given
by 6 copies of $D_4$ root system. This CFT then leads to the construction of an
infinite-dimensional graded module for the umbral group $G^{D_4^{\oplus 6}}$
whose graded characters coincide with the umbral moonshine functions. We also
comment on how one can recover all umbral moonshine functions corresponding to
the Niemeier root systems $A_5^{\oplus 4}D_4$, $A_7^{\oplus 2}D_5^{\oplus 2}$ ,
$A_{11}D_7 E_6$, $A_{17}E_7$, and $D_{10}E_7^{\oplus 2}$.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas