来自爆破方程的 5 维 $\mathcal{N}=1$ 理论中的广义全局对称性
Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
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中文总结 AI 辅助
研究 5 维 $\mathcal{N}=1$ 理论的广义全局对称性，通过爆破方程提取相关数据，包括 1 - 形式对称性的立方自反常及混合反常等，结合超共形指标确定的对称性，判断理论是否有 2 - 群对称性或混合 't Hooft 反常，在多种理论中演示并获新结果。
中文摘要 AI 辅助
五维 $\mathcal{N}=1$ 超共形场理论具有丰富多样的广义全局对称性，包括高形式对称性、2 - 群对称性及其 't Hooft 反常。研究表明这些数据可直接从控制此类理论在 $\Omega$ - 背景下瞬子配分函数的爆破方程中提取。核心对象是经典预因子 $\exp(-V_n)$，其指数的分数部分编码了 1 - 形式对称性的立方自反常以及与瞬子、味、引力和 $\mathrm{SU}(2)_R$ 对称性的混合反常。结合从超共形指标确定的紫外不动点的忠实连续全局对称性，可判断理论是否具有 2 - 群对称性或混合 't Hooft 反常。文中在规范理论及非拉格朗日理论家族中进行了方法演示并得出新结果。
英文摘要
Five-dimensional $\mathcal{N}=1$ superconformal field theories admit a rich variety of generalised global symmetries, including higher-form and 2-group symmetries and their 't$~$Hooft anomalies. We show that this data can be extracted directly from the blow-up equations governing the instanton partition functions of such theories on the $Ω$-background. The central object is the classical prefactor $\exp(-V_n)$ weighting each magnetic flux on the blown-up geometry: evaluated on a background for the electric 1-form symmetry, the fractional parts of its exponents encode the cubic self-anomaly of the 1-form symmetry and its mixed anomalies with the instanton, flavour, gravitational, and $\mathrm{SU}(2)_R$ symmetries. Combined with the faithful continuous global symmetry of the ultraviolet fixed point, determined from the superconformal index, the same data decides whether the theory possesses a 2-group symmetry or a mixed 't$~$Hooft anomaly. We illustrate the method in gauge theories, including $\mathrm{SU}(4)$ and $\mathrm{USp}(4)$ with antisymmetric hypermultiplets and $\mathrm{Spin}(7)$ and $\mathrm{Spin}(8)$ with vector hypermultiplets, as well as in several families of non-Lagrangian theories. New results include the effective prepotentials of the $B_N$ and $B_N^{(1,2,3)}$ families, the cubic 1-form anomalies of the rank-two theories $\mathbb{P}^2\cup\mathbb{F}_3$ and $\mathbb{P}^2\cup\mathbb{F}_6$, and several mixed 1-form--flavour and 1-form--$\mathrm{SU}(2)_R$ anomalies.
发表机构
- Università di Milano-Bicocca（米兰比可卡大学）
- INFN, sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分所）
- The Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University（纳瑞宣大学基础研究院“塔波学术学院”）
机构由 AI 辅助整理，请以论文原文为准。
