Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathrm{SU}(r)$ Vafa-Witten invariants, Ramanujan's continued
  fractions, and cosmic strings   We conjecture a structure formula for the $\mathrm{SU}(r)$ Vafa-Witten
partition function for surfaces with holomorphic 2-form. The conjecture is
based on $S$-duality and a structure formula for the vertical contribution
previously derived by the third-named author using Gholampour-Thomas's theory
of virtual degeneracy loci.
  For ranks $r=2,3$, conjectural expressions for the partition function in
terms of the theta functions of $A_{r-1}, A_{r-1}^{\vee}$ and Seiberg-Witten
invariants were known. We conjecture new expressions for $r=4,5$ in terms of
the theta functions of $A_{r-1}, A_{r-1}^{\vee}$, Seiberg-Witten invariants,
and continued fractions studied by Ramanujan. The vertical part of our
conjectures is proved for low virtual dimensions by calculations on nested
Hilbert schemes.
  The horizontal part of our conjectures give predictions for virtual Euler
characteristics of Gieseker-Maruyama moduli spaces of stable sheaves. In this
case, our formulae are sums of universal functions with coefficients in Galois
extensions of $\mathbb{Q}$. The universal functions, corresponding to different
quantum vacua, are permuted under the action of the Galois group.
  For $r=6, 7$ we also find relations with Hauptmoduln of $\Gamma_0(r)$. We
present $K$-theoretic refinements for $r=2,3,4$ involving weak Jacobi forms.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas