二元群的离散反常

Note on gauge and gravitational anomalies of discrete $Z_N$ symmetries

In this note, we discuss the consistency conditions which a discrete $Z_N$ symmetry should satisfy in order that it is not violated by gauge and gravitational instantons. As examples, we enlist all the $Z_N$ ${\cal R}$-symmetries as well as non-${\cal R}$ $Z_N$ symmetries (N=2,3,4) in the minimally supersymmetric standard model (MSSM) that are free from gauge and gravitational anomalies. We show that there exists non-anomalous discrete symmetries that forbid Baryon number violation up to dimension 6 level (in superspace). We also observe that there exists no non-anomalous $Z_3$ ${\cal R}$-symm…

Anomaly-safe discrete groups

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer from anomalies. We present two different ways that allow one to understand these statements.

On Discrete Anomalies in Chiral Gauge Theories

We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We further exhibit an explicit path to the gapless fermion phase, showing that there is no kinematic obstructi…

离散对称反常与规范耦合统一

Anomalies of Discrete Symmetries and Gauge Coupling Unification

离散对称的异常被定义为路径积分测度的雅可比矩阵。假设在低能量的异常被取消的Green-Schwarz（GS）机制在一个基本的规模，我们调查可能的Kac-Moody水平的异常离散族对称性。作为第一个例子，我们考虑了具有跷跷板机制的最小超对称标准模型中的离散阿贝尔重子数和轻子数对称性，发现规范耦合的普通统一与GS条件不一致，表明可能存在更多的Higgs二重态。我们考虑各种最近提出的超对称模型与非阿贝尔离散族对称。在具有$Q_{6}$族对称性的超对称例子中，GS条件使得规范耦合统一看起来接近普朗克尺度。

反常与离散手征对称性

Anomalies and discrete chiral symmetries

打破无质量多味QCD的U（1）轴对称性的量子反常留下了离散的味单重手征不变性。对于有质量的夸克，这种剩余对称性与强CP破坏参数θ有着密切的联系。一个结果是，如果最轻的夸克是简并的，那么当θ通过π时，就会发生一级跃迁。由此产生的框架有助于澄清，当生根处方外推的口味数量是有效的。

Pocket Formulae for Non-Abelian Discrete Anomaly Freedom

We show that the discrete anomaly constraints governing popular non-Abelian symmetries of use in (e.g.) flavoured, supersymmetric, and dark matter model building typically subdivide into two classes differentiated by the simple restrictions they impose on the number of fields transforming under certain irreducible representations of the relevant groups. These constraints lead us both to generic conclusions for common Beyond-the-Standard-Model constructions (including rather powerful statements for Grand Unified theories) as well as to simplified formulae that can be rapidly applied to determin…

广义反常、QCD₄ 与全息对偶

Generalised anomalies, QCD$_4$, and holography

本文从 D4-D8 系统的全息对偶出发，通过涂抹 D8 膜并构造保持规范不变性的 IIA 型超引力通量表述，推导出无质量 QCD₄ 中离散轴矢对称性与味、重子对称性之间的谷崎混合反常。

Discrete Anomaly Matching for the Pouliot Type Dualities

We compute the 't Hooft anomalies of discrete symmetries in the Pouliot type dual theories and check their anomaly matching conditions. The Pouliot type dual theories we will consider in this paper are two dual pairs; the dual pair of ${\cal N}=1$ supersymmetric theories of a $Spin(7)$ gauge theory with spinors and a $SU(N_f-4)$ gauge theory with a symmetric tensor, fundamentals and singlets, and the other dual pair of ${\cal N}=1$ supersymmetric theories of a $Spin(10)$ gauge theory with a spinor and vectors and a $SU(N_f-5)$ gauge theory with a symmetric tensor, fundamentals and singlets. We…

2-指标手征规范理论

2-index chiral gauge theories

本文系统研究了4维 SU(N) 2-指标手征规范理论的全局对称性与动力学，结合微扰与非微扰方法利用 't Hooft 反常约束其红外相，确定了最可能的对称性破缺模式，并发现少数理论可能流向共形不动点。

Spontaneous Breaking of Gauge Groups to Discrete Symmetries

Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent anomalies. We minimize a number of Higgs potentials that break gauge groups to discrete symmetries of interest, and examine their scalar mass spectra.

通过全局反常消除实现拓扑量子暗物质

Topological Quantum Dark Matter via Global Anomaly Cancellation

本文通过系统枚举离散B±L对称性下的规范-引力全局反常，提出用4维拓扑序或无隙共形场论作为量子暗物质来消除标准模型反常，并发现N_f=3的唯一性及第五种力、任意子激发和拓扑轻子生成等推论。

二十面体群对称性中的轻子味模型和衰变暗物质

Lepton Flavor Model and Decaying Dark Matter in The Binary Icosahedral Group Symmetry

我们提出了一个新的味模型，该模型能很好地描述宇宙线中（衰变）暗物质的间接探测实验。我们不仅证明了A '_{5}对称性能一致地导出夸克和轻子的质量和混合，而且还得到了轻子扇区的一些预言。如果我们假设一个规范单重态费米子衰变的暗物质，它的衰变算符也受到这种对称性的约束，所以只有六维轻子衰变算符才允许达到六维拉格朗日。我们发现PAMELA和Fermi-LAT报道的宇宙线异常现象可以很好地解释为受A '_{5}味对称性控制的衰变暗物质引起的宇宙衰变。