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Vacuum States of the Heterotic String

杂优势链的真空状态

基本信息

批准号：
EP/J010790/1
负责人：
Xenia De La Ossa
金额：
$ 78.22万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ010790%2F1
关键词：
Vacuum States Heterotic String

项目摘要

String theory is believed to be a theory capable of describing all the known forces of nature, and provides a solution to the venerable problem of finding a theory of gravity consistent with quantum mechanics. To a first approximation, the world we observe corresponds to a vacuum of this theory. String theory admits many of these vacuum states and the class that is most likely to describe the observed world are the so-called `heterotic vacua'. Analysing these vacua requires the application of sophisticated tools drawn from mathematics, particularly from algebraic geometry. If history is any guide, the synthesis of these mathematical tools with observations drawn from physics will lead not only to significant progress in physics, but also important advances in mathematics. An example of such a major insight in mathematics, that arose from string theory, is mirror symmetry. This is the observation that within in a restricted class of string vacua, these arise in `mirror pairs'. This has the consequence that certain mathematical quantities, which are both important and otherwise mysterious, can be calculated in a straightforward manner. The class of heterotic vacua, of interest here, are a wider class of vacua, and an important question is to what extent mirror symmetry generalises and how it acts on this wider class.In a more precise description, the space of heterotic vacua is the parameter space of pairs (X,V) where X is a Calabi-Yau manifold and V is a stable holomorphic vector bundle on X. This space is a major object of study in algebra and geometry. String theory tells us that it is subject to quantum corrections. To understand the nature of these corrections is the key research problem in this proposal and any advance in our understanding will have a important impact in both mathematics and physics. By now it is widely understood that string theory and geometry are intimately related with much to be learned from each other, yet this relationship is relatively unexplored in the heterotic string. This fact, together with recent developments that indicate that longstanding problems have recently become tractable, means that the time is right to revisit the geometry of heterotic vacua.

弦理论被认为是一种能够描述自然界所有已知力的理论，并为寻找与量子力学一致的引力理论这一古老问题提供了解决方案。在第一近似下，我们观察到的世界对应于这个理论的真空。弦理论承认许多这样的真空态，而最有可能描述观察到的世界的一类是所谓的“杂合真空”。分析这些真空需要运用从数学，特别是代数几何中提取的复杂工具。如果历史是任何指南，这些数学工具与从物理学中得出的观察结果的综合将不仅导致物理学的重大进展，而且也是数学的重要进展。镜像对称是数学中的一个重要发现，它起源于弦理论。这是观察到在一个有限的弦真空类中，这些出现在“镜像对”中。这使得某些重要而神秘的数学量可以直接计算出来。这里我们感兴趣的杂种真空类是一个更广泛的真空类，一个重要的问题是镜像对称在多大程度上推广以及它如何作用于这个更广泛的真空类。在更精确的描述中，杂种真空空间是对（X，V）的参数空间，其中X是一个Calabi-Yau流形，V是X上的一个稳定的全纯向量丛。这个空间是代数和几何学的主要研究对象。弦理论告诉我们，它会受到量子修正的影响。理解这些修正的性质是这个提议中的关键研究问题，我们理解的任何进展都将对数学和物理产生重要影响。到目前为止，弦理论和几何学之间有着密切的联系，彼此之间有很多东西要学，这一点已被广泛理解，但在杂合弦中，这种关系还相对未被探索。这一事实，加上最近的发展表明，长期存在的问题最近变得容易处理，意味着是时候重新审视杂种优势真空的几何形状。