Extended supersymmetry in gauge theory, gravity and integrable models

规范理论、引力和可积模型中的扩展超对称性

• 批准号: 219718864
• 负责人: Professor Dr. Olaf Lechtenfeld
• 金额: --
• 依托单位: Institut für Physik (IFP)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219718864?language=en
• 关键词: Extended; supersymmetry; gauge; theory; gravity

In the course of this project, we plan to consider the following main tasks:(1) Studying N=1 supersymmetric self-dual electrodynamics in the superspace formalism with chiral auxiliary superfields, including coset scalar superfields into this scheme with the purpose to extend U(N) duality to Sp(2N).(2) Revisiting the problem of constructing the N=2 Born-Infeld action with half-broken N=4 supersymmetry in the approach with chiral auxiliary superfields.(3) Constructing new harmonic superspace formulations of gauge theories in diverse dimensions, including d=3 superconformal Chern-Simons gauge theories and different versions of N=4 SYM theory, and investigating the quantum properties of four-dimensional N=2 supergravity in harmonic superspace.(4) Developing new methods for analyzing the quantum properties of Yang-Mills theories formulated in different admissible gauges and studying the two-loop structure of the low-energy effective action in d=3, N=2 supersymmetric non-Abelian gauge theory.(5) Finding new classical solutions to the Einstein-Chern-Simons equations coupled with matter fields in AdS_5 and identifying the corresponding holographically dual operators on the boundary.(6) Searching for new integrable and non-integrable cosmological and black-hole models which can fit into gauged extended supergavity. (7) Studying quantum mechanics with extended supersymmetry, including superconformal ones, revealing their relation to supersymmetric field theories in higher dimensions, AdS/CFT correspondence and black-hole physics.(8) Constructing new classical and quantum d=1 and d=2 models with deformed N=4 and N=8 supersymmetries in the superfield approach.(9) Constructing d=2 integrable models with a higher integral of motion (besides energy) within the polynomial approach and studying new solutions of the master equations by using symmetric variables. (10) Searching for invariant subvarieties of the full symmetric sl(n)-Toda flow on degenerate orbits, constructing the corresponding phase transition diagrams and generalizing it to Toda systems based on other Lie algebras and coset spaces.(11) Studying the harmonic spheres conjecture linking G-valued Yang-Mills fields on R^4 and harmonic maps of the Riemann sphere into the loop space over G.(12) Applying of non-commutative geometry to the magnetic Bloch theory and the quantum Hall effect as well as extending Dirac quantization to non-smooth observables.Most of these tasks are logical continuations of investigations that were carried out earlier.

（1）在具有手征辅助超场的超空间形式中研究N=1的超对称自对偶电动力学，包括陪集标量超场，目的是将U（N）对偶推广到Sp（2N）。(2)用手征辅助超场的方法重新讨论了N=4超对称半破缺的N=2 Born-Infeld作用量的构造问题。(3)构建了不同维度的规范理论的新的调和超空间表述，包括d=3的超共形Chern-Simons规范理论和不同版本的N=4的SYM理论，并研究了四维N=2的超引力在调和超空间中的量子性质。(4)发展新的方法来分析不同容许规范下杨-米尔斯理论的量子性质，并研究d=3，N=2超对称非阿贝尔规范理论中低能有效作用量的双环结构。(5)在AdS_5中寻找与物质场耦合的Einstein-Chern-Simons方程的新的经典解，并确定边界上相应的全息对偶算子。(6)寻找新的可积和不可积的宇宙学和黑洞模型，以适应规范的扩展超重力。(7)研究具有扩展超对称性的量子力学，包括超共形的，揭示它们与更高维度的超对称场论，AdS/CFT对应和黑洞物理学的关系。(8)用超场方法构造新的具有变形N=4和N=8超对称性的d=1和d=2的经典和量子模型。(9)构造d=2的可积模型与更高的运动积分（除了能量）内的多项式方法和研究新的解决方案的主方程，通过使用对称变量。(10)在退化轨道上寻找全对称sl（n）-户田流的不变子簇，构造相应的相变图，并基于其它李代数和陪集空间将其推广到户田系统. (11)研究了R^4上G值Yang-Mills场的调和球猜想和黎曼球到G上圈空间的调和映射。(12)将非对易几何应用于磁布洛赫理论和量子霍尔效应，并将狄拉克量子化扩展到非光滑观测量。这些任务大多是早期研究的逻辑延续。