Effective field theories, soft theorems and ambitwistor strings

研究方向为散射振幅、弦理论和共形无穷大。散射振幅形成s矩阵，描述粒子从无限过去到无限未来的散射。保形无穷提供了一种方法来理解无限的过去和未来作为初始和最终数据超曲面，从而对s矩阵的构造及其性质（包括对称性）进行几何洞察。特别是，Strominger和合作者最近表明，这些渐近对称性与散射振幅[1]的软定理之间存在明确的关系。导师[2]最近的工作表明，这在双弦理论中具有特别透明和几何的表示。此外，雄心弦理论最近被扩展到包括有效的场理论，如DBI，非线性sigma模型等，它们特别增强了软行为。软行为在s矩阵的构造中是特别有问题的，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（或者是微不足道的），并且服从于许多不存在的定理。然而，多年来，物理学家一直在为这些理论计算s矩阵，使用诸如维度正则化的方法来理解发生的发散，并对关键结构（如红外发散的指数）有详细的了解。这些对于欧洲核子研究中心的截面计算是必不可少的。这些问题中的任何一个的解决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：总体目标是理解潜在的数学结构，并解决以红外问题为中心的s矩阵构建中的关键理论问题，包括软限制和s矩阵的保角表示。在Strominger等人基于场论的技术与导师和合作者开发的ambitwistor弦框架之间创建一个字典。比较两种框架下渐近对称的作用。了解红外扇区在雄心勃勃的框架。了解物理学家的方法如何面对不同红外波段之间的散射问题。在增强软行为的有效场论中会有新的效应，因此这些将提供一个试验场。-研究方法的新颖性：使用雄心弦是牛津大学和合作者的独特之处，并提供了在社区其他地方未广泛使用的强大新技术（[3],[4]）。有效的场论应该表现出相对于传统理论的新行为A.施特罗明格，重力红外结构与规范理论的讲座，物理学报，34 (4):173.05448 .[j]李志强，李志强，李志强，零无穷大下的Ambitwistor字符串和子超前软极限，第1类。引用本文：量子引力学报，2014,44 (5):146.1462L. Mason和D. Skinner，异质扭弦理论，核子。理论物理。生物医学工程学报（2008），35(4):888 - 888。[10]李建军，李建军，李建军，等。激光散射方程的研究进展，光子学报，2014,33(4):559 - 564。该项目属于EPSRC数学科学研究领域，特别是数学物理的子领域。没有公司或合作者参与。

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.