论文标题
关于$ n = 1 $ supersymmetry in $ d = 4 $ dimensions使用SuperSpace Techniques的通用超级/物质/Yang-Mills lagrangian推导的注释
Notes on the derivation of the general supergravity/matter/Yang-Mills Lagrangian for $N=1$ supersymmetry in $d=4$ dimensions using superspace techniques
论文作者
论文摘要
Kählersuperspace以几何方式描述了物质与$ n = 1 $ supersymmetry in $ d = 4 $尺寸的耦合。实现Kähler超空间的一种直接方法是通过$ \ mathrm {u}（1）$ superspace来识别$ \ mathrm {u}（1）$带有Kähler潜力的预能，这是物质（手性）超级领域的函数。在此框架中，超级多重组的组件包含在Superspace的Supervielbein和Torsion Tensor中。此外，通过引入连接$ 1 $ -SU的额外量规结构来制定与Yang-Mills（Vector）多重组的相互作用。在这些注释中，为特定的一组扭转约束解决了$ \ mathrm {u}（1）中的Bianchi身份，从而导致最小的超级型多重倍数。此外，得出了量规部门中比安奇（Bianchi）身份的解决方案，并定义了kählersuperspace。在超级场级别，制定了超级/物质/Yang-Mills系统和超级重力转换的一般动作，并推导了运动方程式。使用对超空间中最低组件的投影，计算了组件场级别的相应的拉格朗日和超级变换，并确定辅助场运动方程。与现有文献相比，这些笔记提供了一般且一致的逐步推导，以$ n = 1 $ supersymmetry在$ d = 4 $尺寸中，通过超级空间技术，对一般超级/物质/yang-mills lagrangian提供了一个独立的和一致的。
The coupling of matter to supergravity with $N=1$ supersymmetry in $d=4$ dimensions is described in a geometric manner by Kähler superspace. A straightforward way to implement Kähler superspace is via $\mathrm{U}(1)$ superspace by identifying the $\mathrm{U}(1)$ pre-potential with the Kähler potential, which is a function of the matter (chiral) superfields. In this framework, the components of the supergravity multiplet are contained in the supervielbein and torsion tensor of superspace. Furthermore, interactions with the Yang-Mills (vector) multiplet are formulated by introducing a connection $1$-superform of an additional gauge structure. In these notes, the Bianchi identities in $\mathrm{U}(1)$ superspace are solved for a particular set of torsion constraints which lead to the minimal supergravity multiplet. Moreover, the solution of the Bianchi identities in the gauge sector is derived and Kähler superspace is defined. At the superfield level, the general action of the supergravity/matter/Yang-Mills system and supergravity transformations are formulated, and the equations of motion are deduced. Using projection to lowest components in superspace, the corresponding Lagrangian and supergravity transformations at the component field level are calculated, and the equations of motion of the auxiliary fields are determined. Compared to existing literature, these notes provide a self-contained and consistent step by step derivation of the general supergravity/matter/Yang-Mills Lagrangian for $N=1$ supersymmetry in $d=4$ dimensions by means of superspace techniques.
