This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds.Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol’nyi-Prasad-Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both Super-Yang-Mills theories, their higher-order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern-Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.

中文翻译：

---

膜有效作用、Kappa 对称性和应用。

这是对膜有效作用、它们的对称性及其一些应用的回顾。它的第一部分涵盖了单一 M 和 D 膜有效作用的 Green-Schwarz 公式，重点关注运动学方面：它们的自由度的识别、世界体积微分同胚和 kappa 对称性的重要性，以实现明显的时空协变性和超对称性，以及在任意壳内超重力背景下明确构造此类动作。第二部分涉及应用。首先，利用卡帕对称性来确定超对称世界体积孤子。这包括它们在平坦和弯曲背景中的显式构造、它们对超对称代数中携带（拓扑）电荷的 Bogomol'nyi-Prasad-Sommerfield (BPS) 态的解释以及超对称性和哈密顿 BPS 界限之间的联系。如果有的话，我会强调使用这些孤子作为黑洞微观模型的组成部分。其次，利用反德西特/共形场论 (AdS/CFT) 对应关系，使用探针近似来推断强耦合规范理论的非平凡动力学。这包括威尔逊环算子的期望值、频谱信息以及一般使用 D 膜探针来近似具有少量自由度的系统与较大系统相互作用的动力学，从而允许双引力描述。最后部分简要讨论了有效的行动对于N D-膜和M2-膜。这包括超杨米尔斯理论、它们的高阶修正和将这些耦合与弯曲背景协变的部分结果，以及最近使用场论、膜结构和 3 代数描述 M2 膜的超对称 Chern-Simons 物质理论考虑因素。