Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Rademacher Sums, the Largest Mathieu Group, and the Holographic
  Modularity of Moonshine   Recently a conjecture has been proposed which attaches (mock) modular forms
to the largest Mathieu group. This may be compared to monstrous moonshine, in
which modular functions are attached to elements of the Monster group. One of
the most remarkable aspects of monstrous moonshine is the following genus zero
property: the modular functions turn out to be the generators for the function
fields of their invariance groups. In particular, these invariance groups
define genus zero quotients of the upper half plane. It is therefore natural to
ask if there is an analogue of this property in the Mathieu case, and at first
glance the answer appears to be negative since not all the discrete groups
arising there have genus zero. On the other hand, in this article we prove that
each (mock) modular form appearing in the Mathieu correspondence coincides with
the Rademacher sum constructed from its polar part. This property, inspired by
the AdS/CFT correspondence in physics, was shown previously to be equivalent to
the genus zero property of monstrous moonshine. Hence we conclude that this
"Rademacher summability" property serves as the natural analogue of the genus
zero property in the Mathieu case. Our result constitutes further evidence that
the Rademacher method provides a powerful framework for understanding the
modularity of moonshine, and leads to interesting physical questions regarding
the gravitational duals of the relevant conformal field theories.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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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: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg