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 \( {\hat{\mathbf{A}}}_{\mathbf{1}} \) CFT at all levels. We find intriguing coincidences such as: (i) for the same level CFTs with \( {\hat{\mathbf{A}}}_{\mathbf{2}} \) and \( {\hat{\mathbf{G}}}_{\mathbf{2}} \) have the same (n, l) values, (ii) for the same level CFTs with \( {\hat{\mathbf{B}}}_{\mathbf{r}} \) and \( {\hat{\mathbf{D}}}_{\mathbf{r}} \) have the same (n, l) values for all r ≥ 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 fifteen “discrete” CFTs; except three all others have Kac-Moody symmetry.

由Mathur-Mukhi-Sen（MMS）程序给出的有理共形场理论的分类方案通过两个数字（（n，l））标识有理共形场理论。n是有理共形场论的特征数。这些字符形成了模块化线性微分方程（也用（n，l）标记）的线性独立解。Wronskian索引l是与Wronskian的零结构相关的非负整数。

在本文中，我们计算了三类众所周知的CFT的（n，l）值。WZW CFT，Virasoro最小模型和\（\ mathcal {N} \） = 1个超级Virasoro最小模型。对于后两个，我们获得Wronskian指数的精确公式。对于WZW CFT，我们获得小级别（最多2个）和所有级别以及所有级别和小级别（最多2个）的精确公式，而其余的则使用计算机程序进行计算。我们发现，所有级别的任何WZW CFT都具有消失的Wronskian索引，\（{\ hat {\ mathbf {A}}} _ {\ mathbf {1}} \） CFT也是如此。我们发现有趣的巧合，例如：（i）对于具有\（{\ hat {\ mathbf {A}}} _ {\ mathbf {2}} \）和\（{\ hat {\ mathbf {G }}} _ {\ mathbf {2}} \）具有相同的（n，l）值，（ii）具有\（{\ hat {\ mathbf {B}}} _ {\ mathbf {r}} \）和\（{\ hat {\ mathbf {d}}} _ {\ mathbf {R}} \）具有相同的（N，L为所有）值[R≥ 5。

对给定（n，l）的所有有理保形场理论进行分类是MMS程序的目标之一。我们可以使用我们的计算来提供部分分类。对于著名的（2 ， 0）的情况下，我们的部分分类结果是完整的分类（三十年前通过MMS实现）。对于（3 ， 0）的情况下，我们的局部分类包括两个无穷级数CFTS的以及15“离散的” CFTS; 除了三个以外，其他所有物体都具有Kac-Moody对称性。