Supersymmetry in curved space

该项目旨在探索弯曲空间中的超对称场论及其一些应用。项目的初始部分是计算广义Spencer上同调，以确定其解生成李超代数的杀戮旋量方程。然后确定包含这样的消灭旋量的几何，并为每个这样的几何确定相应的超对称代数。研究这些超对称代数的酉表示理论，可以确定每个几何中的自然超多重态，从而可以构造超对称场论。这些可以应用于量子场理论的超对称局域化。

The project aims to explore supersymmetric field theories in curved space and some of their applications. An initial part of the project to compute generalised Spencer cohomology in order to determine Killing spinor equations whose solutions generate a Lie superalgebra. One then determines the geometries admitting such Killing spinors and for each such geometry the corresponding supersymmetry algebra. Studying the unitary representation theory of these supersymmetry algebras one determines the natural supermultiplets in each geometry and one can then construct supersymmetric field theories. These can then be applied to supersymmetric localisation of quantum field theories.