Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the identity module in $c=0$ CFTs   It has long been understood that non-trivial Conformal Field Theories (CFTs)
with vanishing central charge ($c=0$) are logarithmic. So far however, the
structure of the identity module -- the (left and right) Virasoro descendants
of the identity field -- had not been elucidated beyond the stress-energy
tensor $T$ and its logarithmic partner $t$ (the solution of the "$c\to 0$
catastrophe"). In this paper, we determine this structure together with the
associated OPE of primary fields up to level $h=\bar{h}=2$ for polymers and
percolation CFTs. This is done by taking the $c\to 0$ limit of $O(n)$ and Potts
models and combining recent results from the bootstrap with arguments based on
conformal invariance and self-duality. We find that the structure contains a
rank-3 Jordan cell involving the field $T\bar{T}$, and is identical for
polymers and percolation. It is characterized in part by the common value of a
non-chiral logarithmic coupling $a_0=-{25\over 48}$.

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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-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: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org