Geometry for String Model Building

“超对称和弦理论的粒子物理和宇宙学”研究计划的主要目的是建立一个强大的英国研究努力，探索弦紧化的数学和物理学。提议的工作具有很强的跨学科方面，并将纳入粒子物理学和宇宙学。这得益于更广泛的国际合作，包括牛津大学和英国帝国理工学院，路德维希-马克西米利安大学/慕尼黑马克斯-普朗克研究所和德国汉堡大学/德西大学，以及美国宾夕法尼亚大学和普林斯顿大学。因此，向EPSRC提交的提案还附有向德国DFG和美国NSF提交的相关提案。弦理论是物理学和数学交界的一个研究领域。它与前沿数学有关，并确实启发了前沿数学，同时它仍然是最有希望的统一物理理论的候选者。通过弦理论，几何学的研究——包括微分几何和代数几何的数学领域——与物理理论的性质直接相关，比如它们的粒子含量或与之相关的宇宙演化。例如，在一些结构中，欧拉数（大致计算几何中“孔”的数量）也决定了相关物理理论中基本粒子族的数量。这种联系导致了物理学和数学之间富有成效的互动，一方面，先进的数学方法被应用于分析弦理论模型，另一方面，物理见解激发了新的数学发展。拟议的国际研究的主题是在这个跨学科领域的中心。弦理论的进步主要依赖于理解如何将先进的数学方法应用于具体的弦理论设置。它还需要进一步发展这些方法以及创建新的数学结构。在进行这些研究的过程中，该计划的主要目标是为回答当代科学中的一个主要问题奠定基础：弦理论真的是一种可行的物理统一理论吗？

The main purpose of the research proposal "The Particle Physics and Cosmology of Supersymmetry and String Theory" is to create a strong UK research effort exploring the mathematics and physics of string compactifications. The proposed work has strong interdisciplinary aspects and will feed into particle physics and cosmology. This is facilitated by a wider, international collaboration which involves Oxford University and Imperial College in the UK, Ludwig-Maximilian University/Max-Planck Institute Munich and University of Hamburg/Desy in Germany and the University of Pennsylvania and Princeton University in the US. Accordingly, this proposal to EPSRC is accompanied by related proposals to DFG in Germany and NSF in the US. String theory is an area of research at the interface between physics and mathematics. It relates to and has indeed inspired cutting edge mathematics and at the same time it remains the most promising candidate for a unifying physics theory. Via string theory the study of geometry - covered by the mathematical areas of differential and algebraic geometry - is directly related to properties of physical theories, such as their particle content or their associated cosmological evolution. For example, in some constructions, the Euler number, roughly counting the number ``holes" in the geometry, also determines the number of families of fundamental particles in the associated physical theory. This link has led to a fruitful interaction between physics and mathematics, with advanced mathematical methods being applied to analyse string theory models on the one hand and physical insights inspiring new mathematical developments on the other hand.The theme of the proposed international research is at the centre of this interdisciplinary area. Progress in string theory crucially relies on understanding how advanced mathematical methods can be applied in concrete string theory setting. It also requires further developing these methods as well as creating new mathematical structures. In pursuing these lines of investigation, the main goal of the proposed programme is to lay the groundwork for answering one of the main question in contemporary science: Is string theory indeed a viable unified theory of physics?