Extended Supersymmetry in One-dimensional Models

点击翻译按钮获取中文摘要

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.