Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Defects, modular differential equations, and free field realization of N
  = 4 VOAs   For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we
show that the residues of the integrands in the $\mathcal{N} = 4$ Schur
indices, which are related to Gukov-Witten type surface defects in the
theories, equal the vacuum characters of rank$G$ copies of $bc \beta \gamma$
systems that provide the free field realization of associated $\mathcal{N} = 4$
VOAs. This result predicts that these residues, as module characters, are
additional solutions to the flavored modular differential equations satisfied
by the original Schur index. The prediction is verified in the $G = SU(2)$
case, where an additional logarithmic solution is constructed.

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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-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: quant-ph
3
The categories of this paper are: physics
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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: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph