The foundations of twistor-string theory

扭弦理论的基础

• 批准号: EP/F016654/1
• 负责人: Lionel Mason
• 金额: $ 36.15万
• 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: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF016654%2F1
• 关键词: foundations; twistor; string; theory

The twistor programme of Roger Penrose was conceived as an approach to quantum gravity. In Einstein's theory of general relativity, the geometry of space-time is dynamical and gives rise to the gravitational field. In order to quantize it, one has to consider what kind of background can be taken for granted if geometry itself is to be subject to quantum fluctuations. The twistor programme is to take twistor space to be the given background and the arena in which the theory that unites quantum theory and gravity is most naturally expressed. If this is to work, it must be possible to reformulate all basic physics in terms of structures on twistor space. Early successes were the encoding not only of linear massless fields, but also non-linear gauge fields and gravitational fields with right handed circular polarization. However, until late 2003, this programme had been stuck not only on the problem of encoding the full non-linear structure of Yang-Mills and gravity when they are not circularly polarized, but also of the systematic incorporation of quantum field theory. Witten's introduction of twistor-string theory was a major step forward that now gives a clear idea as to how these longstanding difficulties might be overcome, at least in the context of perturbation theory.The focus of Witten's paper was not on the twistor programme nor quantum gravity, but on finding new mathematical techniques to study gauge theories, the class of theories underlying the force laws of the standard model of particle physics. The perturbative calculation of gauge theory scattering amplitudes is particularly challenging and current analytical and numerical techniques run out of steam at a point below that required by upcoming experiments at the Large Hadron Collider at CERN. Witten's starting point was the remarkable formulae due to Parke and Taylor for so called `maximal helicity violating' (MHV) gauge theory amplitudes. Despite being a sum of many many Feynman diagrams, these formulae are particularly compact. In the late 1980s, Nair had found a remarkable interpretaion of these amplitudes in a supersymmetric context as integrals over a space of holomorphic curves in super twistor space, a supersymmetric extension of Penrose's original twistor space. Witten's generalisation was to express general gauge theory amplitudes as an integral over the space of all algebraic curves, but now of arbitrary genus and degree, in super-twistor space. These formulae have been largely verified (at least at tree level) and have had a substantial impact on perturbative gauge theory. However, this impact is currently limited by a lack of proper understanding of the foundations of twistor-string theory and by the fact that existing twistor-string theories automatically incorporate conformal supergravity, an unphysical theory that necessarily corrupts quantum calculations.In subsequent work of the PI and collaborators, the existence of conformal supergravity was seen as an opportunity because it contains Einstein gravity. Twistor-string theories were constructed in which the gravitational degrees of freedom are precisely those of N=4 and 8 Einstein supergravity. However, these require further investigation as it is not clear whether these predict the correct scattering amplitudes.The aims of this proposal are to explore the underlying geometry, to provide mathematical foundations for the subject and to find and investigate new twistor string theories that can describe Einstein gravity, or even just gauge theories on their own. It has emerged that the correct mathematical framework for understanding these theories involves exciting new ideas from algebraic and differential geometry such as sheaves of chiral algebras and generalised complex structures. The eventual aims are to develop twistor-string theory as a tool for studying quantum gauge theories, and for studying quantum gravity.

罗杰·彭罗斯的扭量计划被认为是量子引力的一种方法。在爱因斯坦的广义相对论中，时空的几何是动态的，并产生了引力场。为了证明这一点，我们必须考虑，如果几何学本身受到量子涨落的影响，那么什么样的背景可以被视为理所当然。扭量方案是把扭量空间作为给定的背景和竞技场，在这里，把量子理论和引力结合起来的理论得到了最自然的表达。如果这是可行的，就必须有可能用扭量空间的结构来重新表述所有的基本物理学。早期的成功不仅是线性无质量场的编码，也是非线性规范场和右旋圆极化引力场的编码。然而，直到2003年底，这个计划不仅在杨-米尔斯和引力的非圆极化的完整非线性结构的编码问题上，而且在量子场论的系统结合问题上也停滞不前。维滕对扭量-弦理论的介绍是一个重大的进步，现在它为如何克服这些长期存在的困难提供了一个清晰的思路，至少在微扰论的背景下是这样。维滕论文的重点不是扭量计划或量子引力，而是寻找新的数学方法来研究规范理论，粒子物理学标准模型的力定律的基础理论。规范理论散射振幅的微扰计算特别具有挑战性，当前的分析和数值技术在低于欧洲核子研究中心大型强子对撞机即将进行的实验所需的点时就失去了动力。维滕的出发点是帕克和泰勒提出的关于所谓“最大螺旋破坏”（MHV）规范理论振幅的显着公式。尽管是许多费曼图的总和，这些公式特别紧凑。在20世纪80年代后期，Nair发现了一个显着的解释，这些振幅在超对称的背景下，作为积分的空间全纯曲线在超扭量空间，一个超对称的扩展彭罗斯的原始扭量空间。维滕的概括是表达一般规范理论振幅作为一个整体的空间的所有代数曲线，但现在的任意属和程度，在超扭空间。这些公式已经在很大程度上得到了验证（至少在树的水平上），并对微扰规范理论产生了重大影响。然而，由于对扭曲弦理论的基础缺乏正确的理解，以及现有的扭曲弦理论自动地包含了共形超引力，这是一种非物理理论，必然会破坏量子计算。在PI和合作者随后的工作中，共形超引力的存在被视为一个机会，因为它包含了爱因斯坦引力。扭曲弦理论的引力自由度正好是N=4和8的爱因斯坦超引力。然而，这些需要进一步的研究，因为还不清楚这些是否预测了正确的散射振幅。这个提议的目的是探索潜在的几何，为这个主题提供数学基础，并找到和研究新的扭量弦理论，可以描述爱因斯坦引力，甚至只是规范理论本身。它已经出现了正确的数学框架来理解这些理论涉及令人兴奋的新思想，从代数和微分几何，如层的手征代数和广义复杂的结构。最终的目标是发展扭曲弦理论，作为研究量子规范理论和量子引力的工具。

项目成果

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space

• DOI: 10.1007/jhep12(2010)018
• 发表时间: 2010-09
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: L. Mason;David Skinner

Scattering amplitudes and BCFW recursion in twistor space

• DOI: 10.1007/jhep01(2010)064
• 发表时间: 2009-03
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: L. Mason;David Skinner

Celestial amplitudes and conformal soft theorems

天体振幅和共形软定理

• DOI: 10.1088/1361-6382/ab42ce
• 发表时间: 2019
• 期刊: Classical and Quantum Gravity
• 影响因子: 3.5
• 作者: Adamo T

Conformal Field Theories in Six-Dimensional Twistor Space

六维扭量空间中的共形场论

• DOI: 10.48550/arxiv.1111.2585
• 发表时间: 2011
• 作者: Mason L

Gravity, Twistors and the MHV Formalism

• DOI: 10.1007/s00220-009-0972-4
• 发表时间: 2008-08
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: L. Mason;David Skinner