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Notes on index of quantum integrability
Communications in Theoretical Physics ( IF 2.4 ) Pub Date : 2021-03-22 , DOI: 10.1088/1572-9494/abe9aa
Jia Tian 1, 2 , Jue Hou 1 , Bin Chen 1, 2, 3
Affiliation  

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 ${SU}(N)/{SO}(N)$ and ${SO}(2N)/{SO}(N)\times {SO}(N)$. The indexes of these theories are all non-positive except for the case of ${SO}(4)/{SO}(2)\times {SO}(2)$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the ${{\mathbb{CP}}}^{N}$ model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.



中文翻译:

关于量子可积性指标的说明

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${SU}(N)/{SO}(N)$和的量子可积性指数${SO}(2N)/{SO}(N)\times {SO}(N)$。除了 的情况外,这些理论的指标都是非正的${SO}(4)/{SO}(2)\times {SO}(2)$。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:${{\mathbb{CP}}}^{N}$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。

更新日期:2021-03-22
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