A quantum integrability index was proposed in Komatsu et al (2019 SciPost Phys. 7 065). It systematizes the Goldschmidt and Witten’s operator counting argument (Goldschmidt and Witten 1980 Phys. Lett. B 91 392) by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models and . The indexes of these theories are all non-positive except for the case of . Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.

Komatsu等人(2019 SciPost Phys. 7 065)提出了量子积分指数。它通过使用保形对称性将 Goldschmidt 和 Witten 的算子计数论证（Goldschmidt 和 Witten 1980 Phys. Lett. B 91 392）系统化。在这项工作中，我们计算了对称陪集模型和的量子可积性指数。除了 的情况外，这些理论的指标都是非正的。此外，我们将分析扩展到费米子理论，并考虑一个具体的理论：模型与无质量的狄拉克费米子相结合。我们发现此类模型的索引也是非正的。