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String theory approach to problems of strongly coupled gauge theories

解决强耦合规范理论问题的弦理论方法

基本信息

批准号：
EP/G007063/1
负责人：
Marija Zamaklar
金额：
$ 43.99万
依托单位：
Durham University
依托单位国家：
英国
项目类别：
Fellowship
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%2FG007063%2F1
关键词：
String theory approach problems strongly

项目摘要

Most of modern quantum field theory is based on the remarkableframework of Yang and Mills, who used structures that also occur ingeometry to describe the dynamics of elementary particles. However,despite the fact that the predictions of this theory have beenrigorously tested experimentally, its mathematical foundation is stillnot fully understood. Namely, an important open problem exists on howto analytically compute the spectrum of this theory at strong coupling. Though there are computer simulations which reproduce the observed spectrum,a theoretical understanding of it is still missing.The main obstacle in computing the spectrum of Yang-Mills theory, isthat one needs to understand a system at strong coupling; nonatural small parameter exists which would allow for a standardperturbative approach. Some ten years ago, an ingenious conjecturewas proposed by Maldacena on how to address this long-standingproblem. The idea is very simple, though conceptually challenging:instead of analysing the theory in four space-time dimensions of ourworld, he proposed to consider string theory in a higher-dimensional,curved space. He conjectured that this higher-dimensional stringtheory is equivalent to the lower-dimensional theory of Yang and Millsand proposed a specific map between the two. The key point of thismap is that it inverts the coupling between the two theories: hencestrongly coupled (and hard to address) phenomena in one theory aremapped to weakly coupled (and easy to compute) phenomena in the othertheory.Though the conjecture has so far been checked in specific limits, its proof isstill lacking. Recent discoveries of integrable structures inmaximally supersymmetric Yang-Mills theory (N=4 SYM)have introduced new ideas on how one could prove theconjecture. The main goal of my research is to work towards a proof ofthe string/gauge theory correspondence using these insights.The methods which will be used require a combination of severalinterdisciplinary techniques coming from integrability, quantum fieldtheory, string theory and group theory. As such, the project is verychallenging and a construction of the proof is likely to lead to newdevelopments in mathematics and physics.Although the initial conjecture was formulated for a very specificcase of Yang-Mills theory (the N=4 SYM theory) there are strongindications that the ideas should hold much more generally. Pushingthe limits of the conjecture and understanding where it breaks isanother goal of my research. Since the conjecture opened up a conceptuallynew way of looking at field theory and gravitational(i.e. geometrical) phenomena, understanding to what kind of systems itcan be applied will teach us about fundamental properties ofYang-Mills theories.

大多数现代量子场论都是基于杨和米尔斯的可解释框架，他们用同样发生引力的结构来描述基本粒子的动力学。然而，尽管这一理论的预测已经被严格的实验测试，它的数学基础仍然没有完全理解。也就是说，存在一个重要的公开问题，如何解析计算该理论在强耦合的频谱。虽然有计算机模拟再现观察到的光谱，它的理论理解仍然缺失。计算杨-米尔斯理论的光谱的主要障碍是，人们需要了解一个强耦合的系统;非自然的小参数存在，这将允许一个标准的微扰方法。大约10年前，Maldacena提出了一个巧妙的解决方案来解决这个长期存在的问题。这个想法非常简单，尽管在概念上具有挑战性：他建议在更高维的弯曲空间中考虑弦理论，而不是在我们世界的四维时空中分析理论。他指出，这种高维弦理论等价于低维理论，杨和Millsand提出了两者之间的特定映射。这一映射的关键点在于它颠倒了两个理论之间的耦合：从那时起，一个理论中的强耦合（且难以处理）现象被映射到另一个理论中的弱耦合（且易于计算）现象。尽管这一猜想到目前为止已经在特定的范围内得到了检验，但它的证明仍然缺乏。最近在极大超对称杨-米尔斯理论（N=4 SYM）中发现的可积结构为如何证明该猜想提供了新的思路。我研究的主要目标是利用这些观点来证明弦/规范理论的对应性，所使用的方法需要结合来自可积性、量子场论、弦理论和群论的几个跨学科技术。因此，这个项目是非常具有挑战性的，证明的构建很可能会导致数学和物理学的新发展。尽管最初的猜想是针对杨-米尔斯理论（N=4 SYM理论）的一个非常特殊的情况制定的，但有强烈的迹象表明，这些想法应该更普遍地成立。我研究的另一个目标是突破这个猜想的极限，并理解它的突破点。由于该猜想开辟了一种看待场论和引力（即几何）现象的新方法，理解它可以应用于什么样的系统将使我们了解杨-米尔斯理论的基本性质。