Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wronskian Indices and Rational Conformal Field Theories   The classification scheme for rational conformal field theories, given by the
Mathur-Mukhi-Sen (MMS) program, identifies a rational conformal field theory by
two numbers: $(n, l)$. $n$ is the number of characters of the rational
conformal field theory. The characters form linearly independent solutions to a
modular linear differential equation (which is also labelled by $(n, l)$); the
Wronskian index $l$ is a non-negative integer associated to the structure of
zeroes of the Wronskian.
  In this paper, we compute the $(n, l)$ values for three classes of well-known
CFTs viz. the WZW CFTs, the Virasoro minimal models and the $\mathcal{N} = 1$
super-Virasoro minimal models. For the latter two, we obtain exact formulae for
the Wronskian indices. For WZW CFTs, we get exact formulae for small ranks
(upto 2) and all levels and for all ranks and small levels (upto 2) and for the
rest we compute using a computer program. We find that any WZW CFT at level 1
has a vanishing Wronskian index as does the $\mathbf{\hat{A}_1}$ CFT at all
levels. We find intriguing coincidences such as: (i) for the same level CFTs
with $\mathbf{\hat{A}_2}$ and $\mathbf{\hat{G}_2}$ have the same $(n,l)$
values, (ii) for the same level CFTs with $\mathbf{\hat{B}_r}$ and
$\mathbf{\hat{D}_r}$ have the same $(n,l)$ values for all $r \geq 5$.
  Classifying all rational conformal field theories for a given $(n, l)$ is one
of the aims of the MMS program. We can use our computations to provide partial
classifications. For the famous $(2, 0)$ case, our partial classification turns
out to be the full classification (achieved by MMS three decades ago). For the
$(3, 0)$ case, our partial classification includes two infinite series of CFTs
as well as seven ``discrete'' CFTs; except two all others have Kac-Moody
symmetry.

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The categories of this paper are: math
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga