Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher string functions, higher-level Appell functions, and the
  logarithmic ^sl(2)_k/u(1) CFT model   We generalize the string functions C_{n,r}(tau) associated with the coset
^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau)
associated with the coset W(k)/u(1) of the W-algebra of the logarithmically
extended ^sl(2)_k conformal field model with positive integer k. The higher
string functions occur in decomposing W(k) characters with respect to level-k
theta and Appell functions and their derivatives (the characters are neither
quasiperiodic nor holomorphic, and therefore cannot decompose with respect to
only theta-functions). The decomposition coefficients, to be considered
``logarithmic parafermionic characters,'' are given by A_{n,r}(tau),
B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra
characters of the (p=k+2,1) logarithmic model. We study the properties of
A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string
functions C_{n,r}, and evaluate the modular group representation generated from
A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular
transformations of the higher-level Appell functions and the associated
transcendental function Phi.

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The categories of this paper are: supr-con
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: eess