论文标题
关于量子整合性索引的注释
Notes on index of quantum integrability
论文作者
论文摘要
在\ cite {kms}中提出了量子集成性索引。它通过使用保形对称性来系统地化Goldschmidt和Witten的操作员计数参数\ Cite {Gw}。在这项工作中，我们计算对称coset模型$ {su（n）}/{so（n）} $和$ SO（2n）/{so（so（n）\ times so（n）} $的量子集成性索引。这些理论的索引都是非阳性的，除了$ {so（4）}/{so（2）\ times so（2）} $的情况。此外，我们将分析扩展到具有费米子的理论，并考虑一个具体的理论：$ \ mathbb {cp}^n $模型与无质量的dirac fermion相结合。我们发现，这类模型的索引也是非阳性的。
A quantum integrability index was proposed in \cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \cite{GW} 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.
