Extended Supersymmetry in One-dimensional Models

一维模型中的扩展超对称性

• 批准号: 446598760
• 负责人: Professor Dr. Olaf Lechtenfeld
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/446598760?language=en
• 关键词: Extended; Supersymmetry; dimensional; Models

Based upon superfield methods, including harmonic superspace ones, we will construct new models of supersymmetric mechanics, at the classical and the quantum level, for both one-particle and many-particle cases. For their superfield construction, we will exploit various types of N=2, N=4 and N=8 supermultiplets, including semi-dynamical spinning multiplets, nonlinear multiplets, and mirror multiplets. We plan to quantize some of the constructed models and study their quantum spectra.In particular, we will consider the following main tasks: - Setting up models of deformed N=8 supersymmetric mechanics composed out of two or more different multiplets, with inquiring the ensuing target-space geometry. Inspecting these models on the presence of superconformal symmetries and hidden worldline realizations of the supergroup SU(4|2);- Constructing and quantizing massive superfield matrix models with U(n) gauge symmetry;- Constructing and studying new interacting dynamical and semi-dynamical nonlinear N=4 supermultiplets;- Constructing N=4 superextensions of trigonometric and elliptic Calogero models, as well as their deformations by oscillator-type potentials, with making use of the superfield gauging approach and semi-dynamical multiplets. Generalizations to the case of N=8, d=1 supersymmetry.The studies will be carried out in close cooperation between Russian and German scientists involved in the project.

基于超场方法，包括调和超空间方法，我们将在经典和量子水平上针对单粒子和多粒子情况构建新的超对称力学模型。对于超场构造，我们将利用各种类型的 N=2、N=4 和 N=8 超多重态，包括半动态旋转多重态、非线性多重态和镜像多重态。我们计划量化一些构建的模型并研究它们的量子光谱。特别是，我们将考虑以下主要任务： - 建立由两个或多个不同多重态组成的变形N=8超对称力学模型，并询问随后的目标空间几何形状。检查这些模型是否存在超共形对称性和超群 SU(4|2) 的隐藏世界线实现；- 构造和量化具有 U(n) 规范对称性的大规模超场矩阵模型；- 构造和研究新的相互作用动力和半动力非线性 N=4 超多重态；- 构造三角和椭圆 Calogero 模型的 N=4 超扩展， 以及利用超场测量方法和半动态多重态通过振荡器型势引起的变形。对 N=8、d=1 超对称情况的推广。研究将在参与该项目的俄罗斯和德国科学家的密切合作下进行。