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朗道-金茨堡/共形场论（LG/CFT）对应提供第一个精确的数学陈述和几何证明，这是一种物理驱动的原理，将代数几何中的超曲面奇点与共形场论中的顶点代数表示联系起来。这里开发的形式主义有望澄清对应关系的本质，并直接导致超越简单奇点的概括，并提供一个字典将 CFT 方法翻译为奇点理论，反之亦然。这些成果将进一步巩固澳大利亚作为纯数学和数学物理研究国际领导者的声誉。