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

本项目涉及超对称量子场理论中真空模空间的研究。量子理论的零能凝聚集或真空模空间包含丰富的代数几何结构。对于一大套超对称量子理论，这种结构与李代数中的幂零变元有关。这些幂零变体在数学文献中对于经典李代数是很好的理解的，研究在物理背景下对这种结构和相关结构的解释是本项目的主要目的。超对称量子场理论也被解释为超弦理论嵌入的低能动力学。这些嵌入、量子场理论、真空模空间的几何以及其中所有的潜在推广之间的相互作用是人们关注的中心领域。

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.