Topological defects in conformal field theory and string theory

共形场论和弦理论中的拓扑缺陷

• 批准号: EP/E005047/1
• 负责人: Ingo Runkel
• 金额: $ 25.65万
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE005047%2F1
• 关键词: Topological; defects; conformal; field; theory

The current view of theoretical physics on the workings of Nature is based on two main pillars: general relativity, which describes physics at large scales, like the solar system and beyond, and quantum field theory, which describes the microscopic constituents of matter, like electrons and quarks. Both theories are in perfect agreement with experiment, but to date no mathematically consistent unified formulation, which includes both these theories as appropriate limits, has been found. There are, of course, candidates, and one such candidate is called string theory. While in quantum field theory one thinks of the fundamental particles, e.g. the electrons, as point-like without an extend in any direction of space, in string theory the fundamental particle is a tiny loop. String theory is mathematically highly involved, and it has been impossible so far to make unambiguous contact between experiments and predictions of string theory. The aim of the project is to understand better the mathematical foundations of string theory, in particular its symmetries. This is to be achieved with the help of so-called two-dimensional conformal quantum field theory. The latter describes how the strings, i.e. the tiny loops mentioned above, move in space. In this project the conformal field theory will be investigated in great detail. This will, for example, allow one to understand precisely how a loop of string can get deformed into a figure eight and then split into two loops, or how such a loop can break open at one point and then move in space as a piece of string with two loose ends.This project will provide one more piece in the big puzzle whose ultimate goal is to decide, in the positive or in the negative, if string theory can provide the desired unified description of all the forces we see in Nature.

理论物理学对自然运作的当前观点基于两个主要支柱：一般相对论，它在大规模上描述了太阳系及其他等大规模的物理，以及描述物质的显微镜组成部分，例如电子和夸克。这两种理论都与实验完全吻合，但迄今为止，还没有发现在数学上一致的统一配方，包括这两种理论在适当的范围内。当然，有候选人，其中一个候选人称为弦理论。在量子场理论中，人们认为基本粒子，例如电子，如点状而没有空间的任何方向，在字符串理论中，基本粒子是一个微小的循环。字符串理论在数学上高度参与，到目前为止，无法在实验和弦理论的预测之间实现明确的接触。该项目的目的是更好地理解字符串理论的数学基础，尤其是其对称性。这是在所谓的二维形成形式量子场理论的帮助下实现的。后者描述了字符串，即上述小环在太空中如何移动。在这个项目中，将详细研究保形场理论。 This will, for example, allow one to understand precisely how a loop of string can get deformed into a figure eight and then split into two loops, or how such a loop can break open at one point and then move in space as a piece of string with two loose ends.This project will provide one more piece in the big puzzle whose ultimate goal is to decide, in the positive or in the negative, if string theory can provide the desired unified description of all the forces we see in Nature.