Exact Results in Supersymmetric Quantum Field Theories

超对称量子场论的精确结果

• 批准号: 1818702
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1818702
• 关键词: Exact; Results; Supersymmetric; Quantum; Field

In recent years new techniques have allowed exact calculations in quantum field theories to be performed. This allows quantum field theories to be investigated beyond the weak coupling regime where they may be defined as an asymptotic series in the coupling constant generated by Feynman diagrams. The aim of this thesis is to apply these new techniques in novel areas to help build theoretical understanding.Supersymmetric localisation is an example of one of these new techniques. It allows infinite dimensional Feynman integrals to be reduced to finite dimensional integrals over a compact group. Many models with supersymmetry are amenable to this technique. In particular, many three dimensional partition functions related to the ABJM model, a conjectured fundamental worldvolume theory on the M branes of M theory, can be localised. It has also been argued that three dimensional partition functions can be obtained as a suitable limit of the "superconformal index" of appropriate four dimensional superconformal field theories, which are expressed as similar finite dimensional integrals. In order to investigate the ABJM model we will investigate this link in order to perform exact calculations for quantum field theories related to the ABJM model, but defined on novel manifolds.

近年来，新技术使得量子场论中的精确计算成为可能。这使得量子场论能够在弱耦合范围之外进行研究，在弱耦合范围内，它们可以被定义为由费曼图生成的耦合常数的渐近级数。本论文的目的是将这些新技术应用于新领域，以帮助建立理论理解。超对称定位就是这些新技术之一的例子。它允许将无限维费曼积分简化为紧群上的有限维积分。许多具有超对称性的模型都适用于这种技术。特别是，与 ABJM 模型（M 理论的 M 膜上的猜想的基本世界体积理论）相关的许多三维配分函数可以被局部化。也有人认为，可以获得三维配分函数作为适当的四维超共形场论的“超共形指数”的合适极限，其被表示为类似的有限维积分。为了研究 ABJM 模型，我们将研究此链接，以便对与 ABJM 模型相关但定义在新颖流形上的量子场论进行精确计算。