arXiv 1802.047902018-02-13hep-thcond-mat.str-el

探索2-群整体对称性

Exploring 2-Group Global Symmetries

Clay Cordova, Thomas T. Dumitrescu, Kenneth Intriligator

备注：: 137 pages, 2 figures
DOI：: 10.1007/JHEP02(2019)184

摘要：

我们分析了具有连续2群整体对称性的四维量子场论。在它们的电荷水平上，这种对称性等同于连续味对称性或时空对称性与1-形式全局对称性$U(1)^{(1)}_B$的乘积，后者产生于守恒的2-形式电流$J_B^{(2)}$。相反，2群对称性的特征在于变形的电流代数，量子化的结构常数，这使得两个味道电流或应力张量融合成$J_B^{(2)}$。这导致了非常规的沃德恒等式，它限制了自发的2群对称性破缺和重整化群流的其他方面。如果$J_B^{(2)}$耦合到一个2-形式的背景规范场$B^{(2)}$，2-群流代数修改了$B^{(2)}$在背景规范变换下的行为。它的变换规则与Green-Schwarz机制的形式相同，但只涉及耦合到其他2群流的背景规范场或重力场。这使得在2群背景规范场中使用格林-施瓦茨反项可以部分地消除可约的t Hooft反常。不能取消的部分被重新解释为涉及$U(1)_B^{(1)}$的混合全局异常，并从拓扑和无质量自由度中获得贡献。2群对称性理论是通过测量适当的混合特胡夫特异常的阿贝尔味对称性而构建的，这导致了许多简单而明确的例子。它们中的一些具有携带$U(1)_B^{(1)}$电荷的动力学弦激发，并且2群对称性决定了这些弦的世界片上的某些t Hooft异常。最后，我们指出，全息理论与2群的整体对称性有一个散装的动力学规范场，参与传统的格林-施瓦茨机制的描述。

英文摘要：

We analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry $U(1)^{(1)}_B$, which arises from a conserved 2-form current $J_B^{(2)}$. Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into $J_B^{(2)}$. This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If $J_B^{(2)}$ is coupled to a 2-form background gauge field $B^{(2)}$, the 2-group current algebra modifies the behavior of $B^{(2)}$ under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible 't Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving $U(1)_B^{(1)}$ and receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed 't Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry $U(1)_B^{(1)}$ charge, and 2-group symmetry determines certain 't Hooft anomalies on the world sheets of these strings. Finally, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文