Proving the Landau-Ginzburg/Conformal Field Theory correspondence

证明朗道-金兹堡/共形场论对应关系

• 批准号: DP210101502
• 负责人: Dr Daniel Murfet
• 金额: $ 27.96万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-12-31 至 2025-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210101502
• 关键词: Proving; Landau; Ginzburg; Conformal; Field

This project aims to provide the first precise mathematical statement and geometric proof of the Landau-Ginzburg/Conformal Field Theory (LG/CFT) correspondence for simple singularities, a physically motivated principle that relates hypersurface singularities in algebraic geometry to representations of vertex algebras in conformal field theory. The formalism developed here is expected to clarify the nature of the correspondence and lead directly to generalisations beyond simple singularities, as well as provide a dictionary to translate methods of CFT into singularity theory and vice versa. These results will further cement Australia's reputation as an international leader in pure mathematics and mathematical physics research.

该项目旨在为简单奇点的Landau-Ginzburg/保形场理论（LG/CFT）提供第一个精确的数学陈述和几何证明，这是简单奇异性的对应关系，这是一种具有物理动机的原理，该原理将代数几何学中的超出表面奇异性与certortex algebras在Gelgebras中的形式相关联。预计此处开发的形式主义将阐明对应关系的性质，并直接导致简单奇点以外的概括，并提供了将CFT方法转化为奇异性理论的词典，反之亦然。这些结果将进一步巩固澳大利亚作为纯数学和数学物理学研究的国际领导者的声誉。