Structure in the moduli space of vacua of low dimensional supersymmetric quantum

本课题研究超对称量子场理论中真空的模空间。量子理论的零能量组态或真空模空间包含了丰富的代数几何结构。对于一个大的超对称量子理论集，这种结构与李代数中的幂零变异有关。这些幂零变量在数学文献中被很好地理解为经典李代数，在物理背景下对这一和相关结构的解释的研究是本项目的主要目的。超对称量子场理论也可以解释为超弦理论嵌入的低能动力学。这些嵌入之间的相互作用，量子场理论，真空模空间的几何，以及其中所有的潜在推广，是关注的中心领域。

This Project involves the investigation of the moduli space of vacua of supersymmetricquantum eld theories. The sets of zero-energy congurations, or moduli space of vacua, of a quantumeld theory contains rich algebro-geometric structure. For a large set of supersymmetric quantumeld theories this structure is related to nilpotent varieties in Lie algebras. These nilpotent varietiesare well understood for the classical Lie algebras in the mathematical literature and investigation ofthe interpretation of this and related structures in a physical context is the main aim of this project.The supersymmetric quantum eld theories also have an interpretation as the low energy dynamics ofsuperstring theory embeddings. The interplay between these embeddings, the quantum eld theories,the geometry of the moduli spaces of vacua, and potential generalizations of all therein, is the centralarea of concern.