arXiv 1702.012542017-02hep-th

$Ω$ -形变$\mathcal N=2$理论中的手征迹关系

Chiral trace relations in $Ω$-deformed $\mathcal N=2$ theories

Matteo Beccaria, Alberto Fachechi, Guido Macorini

备注：: 36 pages. v2 references added
DOI：: 10.1007/JHEP05(2017)023

摘要：

我们考虑四维（纯的或质量变形的）中的$\mathcal N=2$ $SU(2)$规范理论，并讨论在一般$Ω$ -变形的存在下最简单的手征观测量的性质。我们计算它们的等变本地化和分析的结构的精确瞬子修正的经典手征环关系。我们预测的精确关系，有效的在所有瞬子数之间的痕迹$\langle\text{Tr}φ^{n}\rangle$，其中$φ$是标量场的规范多重态。在Nekrasov-Shatashvili极限中，这种关系可以用可用的量化的Seiberg-Witten曲线来解释。相反，充分的两个参数的变形享有新的功能和环的关系，需要非平凡的额外的导数项的模块化参数。简要讨论了高秩群，强调非因式分解由于$Ω$ -变形的算子。最后，结构的变形环关系的$\mathcal N=2^{\star}$理论分析的角度来看，Alday-Gaiotto-Tachikawa对应证明一致性以及一些有趣的普遍性属性。

英文摘要：

We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $Ω$-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces $\langle\text{Tr}φ^{n}\rangle$, where $φ$ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the $Ω$-deformation. Finally, the structure of the deformed ring relations in the $\mathcal N=2^{\star}$ theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties.

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