Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossing, Modular Averages and $N \leftrightarrow k $ in WZW Models   We consider the construction of genus zero correlators of $SU(N)_k$ WZW
models involving two Kac Moody primaries in the fundamental and two in the
anti-fundamental representation from modular averaging of the contribution of
the vacuum conformal block. In cases where we find the orbit of the vacuum
conformal block to be finite, modular averaging reproduces the exact result for
the correlators. In other cases, we perform the modular averaging numerically,
the results are in agreement with the exact answers. We find a close
relationship between the modular averaging sums of the theories related by
level rank duality. We establish a one to one correspondence between elements
of the orbits of the vacuum conformal blocks of dual theories. The
contributions of paired terms to their respective correlators are simply
related. One consequence of this is that the ratio between the OPE coefficients
associated with dual correlators can be obtained analytically without
performing the sums involved in the modular averagings. The pairing of terms in
the modular averaging sums for dual theories suggests an interesting connection
between level rank duality and semi-classical holographic computations of the
correlators in the theories.

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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph