Anomaly in RTT relation for DIM algebra and network matrix models
Anomaly in RTT relation for DIM algebra and network matrix models
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DIM 代数和网络矩阵模型的 RTT 关系异常
DOI：
10.1016/j.nuclphysb.2017.03.003
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Y. Ohkubo and Y. Zenkevich
中科院分区：
文献类型：
--
作者：
H. Awata;H. Kanno;A. Mironov;A. Morozov;A. Morozov;Y. Ohkubo and Y. Zenkevich
我们讨论了ARXI：1608.05351最近提出的关于将RTT关系推广到网络矩阵模型的建议。我们证明了这些模型中的RTT关系被一个非平凡的，但本质上是阿贝尔反常共循环所修正，我们显式地评估了量子环状代数的自由场表示。在q变形的共形块体和它的5d/6d规范理论对应的5 d/6 d规范理论中，即非微扰的Nekrasov函数中，编织起了作用。因此，它定义了它们的模性质和对称性。我们展示了如何使用与规范理论中的反常匹配条件有点类似的结构来抵消反常。我们还描述了仿射杨氏函数(4D Nekrasov函数)的奇异极限，它打破了谱对偶。
We discuss the recent proposal of arXiv: 1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q-deformed conformal block and its 5 d/6 d gauge theory counterpart, ie the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions), which breaks the spectral duality.