Effective field theories, soft theorems and ambitwistor strings

这项研究将在散射幅度、弦理论和共形无穷大领域进行。散射幅度形成了描述粒子从无限的过去到无限的未来的散射的S矩阵。共形无穷给出了一种将无限的过去和未来理解为初始和最终数据超曲面的方法，给出了S矩阵的构造及其性质(包括对称性)的几何洞察。特别是，Strominger和他的合作者最近证明，这些渐近对称性和散射幅度的软定理之间存在明显的关系[1]。主管[2]最近的工作表明，这在超弦理论中有一个特别透明和几何的表示。此外，超弦理论最近已经扩展到包括有效场论，如dBI，非线性西格玛模型等，它们具有特别增强的软行为。软行为在S矩阵的构造中特别成问题，事实上，许多纯数学家会说，严格地说，无质量理论的S矩阵不存在(或微不足道)，并受制于许多禁忌定理。然而，物理学家多年来一直在使用维正则化等方法计算此类理论的S矩阵，以解释发生的发散，并详细了解关键结构，如红外发散的指数。这些对于计算欧洲核子研究中心的横截面是必不可少的。解决这些问题中的任何一个都将对这些理论的数学和物理应用产生重大的潜在影响。-目的和目标：首要目标是了解基本的数学结构，并解决围绕红外问题(包括软限制和S矩阵的保形表示)构建S矩阵的关键理论问题。i.在基于场论的施特罗明格技术之间建立一本词典。Ii.比较两个框架中渐近对称性的作用。ii.理解ambitwistor框架内的红外扇区。iv.了解物理学家的方法如何面对不同红外线扇区之间的散射问题。V.在具有增强的软行为的有效场理论中将会有新的效应，因此这些将提供试验场。-研究方法的新颖性：雄心弦的使用是牛津大学的小组和合作者所独有的，并提供了在其他社区中没有广泛使用的强大的新技术([3]，[4])。有效场论应该表现出相对于更传统的理论的新的行为。[1]A.Strominger，关于引力和规范理论的红外结构的讲座，arxiv：1703.05448。[2]Y.Geyer，A.E.Lipstein和L.Mason，Ambitwistor弦在零无限和次弯曲软极限，类。量子引力32,055003(2014年)，arxiv：1406.1462。[3]L·梅森和D·斯金纳，异质扭弦理论，核。太棒了。B795(2008)105，ARXIV：0708.2276。[4]L.Mason和D.Skinner，Ambitwistor弦和散射方程，JHEP 07(2014)048，arxiv：1311.2564。本项目属于EPSRC数学科学研究领域，特别是数学物理学的子领域。不会涉及任何公司或合作者。

The research will be in the area of scattering amplitudes, (ambitwistor) string theory and conformal infinity. Scattering amplitudes form the S-matrix that describes the scattering of particles from the infinite past to the infinite future. Conformal infinity gives a method to understand the infinite past and future as initial and final data hypersurfaces giving a geometric insight into the construction of the S-matrix and its properties, including symmetries. In particular it has recently been shown by Strominger and collaborators that there is a clear relationship between these asymptotic symmetries and soft theorems for scattering amplitudes [1]. Recent work of the supervisor [2] shows that this has a particularly transparent and geometric representation in ambitwistor string theories. Furthermore, ambitwistor string theories have recently been extended to encompass effective field theories such as DBI, nonlinear sigma models, etc., that have particularly enhanced soft behaviour.Soft behaviour is particularly problematic in the construction of the S-matrix, and indeed many pure mathematicians will say that rigourously speaking the S-matrix for massless theories does not exist (or is trivial) and is subject to a number of no-go theorems. However, physicists have been computing the S-matrix for such theories for years using methods such as dimensional regularization to make sense of divergences that occur and have a detailed understanding of key structures such as the exponentiation of infrared divergences. These are essential for calculations of cross sections at CERN. Resolution of any of these issues would have a major potential impact both on the mathematics of these theories and on their physical applications.- Aims and objectives:The overarching aims are to understand underlying mathematical structures and to resolve key theoretical issues in the construction of the S-matrix centred around infrared problems including soft limits and the conformal representations of the S-matrix.I. To create a dictionary between the field theory based technology of Strominger et. al., and the ambitwistor string framework developed by the supervisor and collaborators.II. To compare the action of asymptotic symmetries in the two frameworks.III. To understand infrared sectors within the ambitwistor framework.IV. To gain an understanding of how physicist's approaches confront the issues of scattering between different infrared sectors.V. There will be novel effects in effective field theories with enhanced soft behaviour and so these will provide a testing ground.- Novelty of the research methodology:The use of ambitiwistor strings is unique to the group in Oxford and collaborators and provides powerful new techniques not widely used in the rest of the community ([3], [4]). Effective field theories should exhibit novel behaviours relative to more conventional theories.[1] A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448.[2] Y. Geyer, A. E. Lipstein, and L. Mason, Ambitwistor strings at null infinity and subleading soft limits, Class. Quantum Gravity 32, 055003 (2014), arXiv:1406.1462.[3] L. Mason and D. Skinner, Heterotic twistor-string theory, Nucl. Phys. B795 (2008) 105, arXiv:0708.2276. [4] L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048, arXiv:1311.2564.This project falls within the EPSRC Mathematical Sciences research area, and in particular the sub-area of Mathematical Physics.No companies or collaborators will be involved.