Algebraic structures in topological field theory

拓扑场论中的代数结构

• 批准号: 0906369
• 负责人: Ezra Getzler
• 金额: $ 10.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906369&HistoricalAwards=false
• 关键词: Algebraic; structures; topological; field; theory

In quantum field theory, backgrounds with boundary are equivalent to their double, thought of as an oriented manifold with an orientation reversing involution (orientifold). For example, studying two-dimensional topological field theory in this way, one obtains a powerful approach to open/closed topological field theory. In this project, we will study the role of Z/2-equivariant homotopy and Z/2-equivariant Beilinson-Deligne/Cheeger-Simons cohomology in the formulation of topological field theories on manifolds with boundary, as well as in supergravity.Topological field theories arise in many places in theoretical physics and mathematics (and indeed in the theory of quantum computers). We are interested in understanding better the role of boundaries in the topological field theories that occur in supergravity theory, an important extension of Einstein's theory of General Relativity. Ultimately, boundaries in supergravity are related to problems in cosmology, including the many-worlds interpretation of quantum theory.

在量子场论中，有边界的背景等价于它们的二重，被认为是一个有方向反转对合（orientifold）的定向流形。例如，以这种方式研究二维拓扑场论，人们获得了开/闭拓扑场论的有力方法。在这个项目中，我们将研究Z/2-等变同伦和Z/2-等变Beilinson-Deligne/Cheeger-Simons上同调在有边界流形上的拓扑场论的表述中的作用，以及在超引力中的作用。拓扑场论出现在理论物理和数学的许多地方（实际上在量子计算机理论中）。我们有兴趣更好地理解边界在超引力理论中的拓扑场论中的作用，超引力理论是爱因斯坦广义相对论的重要扩展。最终，超引力的边界与宇宙学中的问题有关，包括量子理论的多世界解释。