Unravelling the Non-Perturbative Structure of Gauge Theory

揭示规范理论的非微扰结构

基本信息

批准号：
EP/C539532/1
负责人：
Bogdan Stefanski
金额：
$ 34.5万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FC539532%2F1
关键词：
Unravelling Non Perturbative Structure Gauge

项目摘要

A century ago Max Planck postulated that energy is not a continuous quantity, but rather that it comes in discrete units called quanta. These are so small that we do not normally see their effect in our day-to-day life. Nonetheless they fundamentally alter the properties of a theory. This discretisation of the energy, and other quantities, in a classical theory, is known as quantisation. It has been carried out for electromagnetic interactions, as well as for nuclear forces, known collectively as gauge theories. The predictions made by these quantum gauge theories have been matched with experiments to a spectacular degree of precision.For example, the gauge theory of nuclear forces predicts that protons and neutrons are composed of extremely small particles called quarks, which have since been found experimentally. Quarks are different from other particles such as electrons or protons, in that they do not occur on their own. They interact so strongly with one another that a single quark very quickly attracts other quarks to form observed particles such as protons or neutrons. This property, known as confinement, occurs because of the strong, or non-perturbative, nature of nuclear interactions. At present we have no way of deriving from the gauge theory of nuclear interactions how confinement happens. It is one of the big challenges of theoretical physics today.In an independent development, twenty years after Planck's discovery, Einstein formulated a theory of gravity known as General Relativity (GR), which generalised Newton's law of gravity. In GR spacetime is curved by matter, such as the earth, and it is this curvature that makes objects 'fall' under gravity. GR too has been verified in many experiments. However, GR is a classical theory, with energy being a continuous quantity.Given the success of quantising gauge theories, physicists tried to quantise GR. It turns out that the usual quantisation procedure cannot be applied to GR! But energy is a universal quantity in physics; it cannot be that some parts of the physical world, such as the atom are described by theories in which energy is quantised, while others, describing planets and stars are described by theories in which energy in continuous! The problem of quantising gravity has become one of the central theoretical problems in physics.An alternative way to quantise gravity has been to use string theory. In this approach, fundamental particles of nature (such as electrons, quarks or gravitons) are not particles at all but rather strings. We have not observed these strings to date because they are very small indeed. So far, the acceptance of string theory comes from the theoretical fact that they give a consistent quantum gauge and gravity theory.Recently, the two, apparently very different, problems of quantising gravity and explaining confinement have been related to one another via the gauge/string correspondence. This incredible result, predicted some 30 years ago by 't Hooft and recently presented by Maldacena, shows that a theory of gravity can be described by a theory of nuclear-like interactions! This correspondence is a fascinating bridge between two of the most challenging problems in modern theoretical physics. I believe that this correspondence can teach us a great deal about the nature of confinement in gauge theory on the one hand, and about the quantisation of gravity on the other.In my work I intend to use the gauge/string correspondence to learn about gauge theory phenomena such as confinement. In particular, I intend to find out how a theory of gravity can re-arrange itself into a theory of gauge interactions. In doing this I will be paying particular attention to the 'stringy' nature of the gravitational theory. Initially, my work will focus on gauge theories which are more symmetric than the theory of nuclear interactions. Despite being more symmetric, such theories possess many similarities with those in the real world. Since the procedure I propose for understanding this re-arrangement does not rely explicitly on the extra symmetries present in the gauge theory, already for such theories I expect to learn a great deal about gauge theory behaviour.Once an understanding of this re-arrangement of string theory into a gauge theory is understood for the more symmetric theories, I intend to apply it to gauge theories with less symmetry, in order to learn more about the gauge theory of nuclear interactions. Finding out how the 'stringy' gravity theory re-organises itself into these realistic gauge theories, I believe, will teach us about non-perturbative gauge theory dynamics such as confinement.A century ago Max Planck postulated that energy is not a continuous quantity, but rather that it comes in discrete units called quanta. These are so small that we do not normally see their effect in our day-to-day life. Nonetheless they fundamentally alter the properties of a theory. This discretisation of the energy, and other quantities, in a classical theory, is known as quantisation. It has been carried out for electromagnetic interactions, as well as for nuclear forces, known collectively as gauge theories. The predictions made by these quantum gauge theories have been matched with experiments to a spectacular degree of precision.For example, the gauge theory of nuclear forces predicts that protons and neutrons are composed of extremely small particles called quarks, which have since been found experimentally. Quarks are different from other particles such as electrons or protons, in that they do not occur on their own. They interact so strongly with one another that a single quark very quickly attracts other quarks to form observed particles such as protons or neutrons. This property, known as confinement, occurs because of the strong, or non-perturbative, nature of nuclear interactions. At present we have no way of deriving from the gauge theory of nuclear interactions how confinement happens. It is one of the big challenges of theoretical physics today.In an independent development, twenty years after Planck's discovery, Einstein formulated a theory of gravity known as General Relativity (GR), which generalised Newton's law of gravity. In GR spacetime is curved by matter, such as the earth, and it is this curvature that makes objects 'fall' under gravity. GR too has been verified in many experiments. However, GR is a classical theory, with energy being a continuous quantity.Given the success of quantising gauge theories, physicists tried to quantise GR. It turns out that the usual quantisation procedure cannot be applied to GR! But energy is a universal quantity in physics; it cannot be that some parts of the physical world, such as the atom are described by theories in which energy is quantised, while others, describing planets and stars are described by theories in which energy in continuous! The problem of quantising gravity has become one of the central theoretical problems in physics.An alternative way to quantise gravity has been to use string theory. In this approach, fundamental particles of nature (such as electrons, quarks or gravitons) are not particles at all but rather strings. We have not observed these strings to date because they are very small indeed. So far, the acceptance of string theory comes from the theoretical fact that they give a consistent quantum gauge and gravity theory.Recently, the two, apparently very different, problems of quantising gravity and explaining confinement have been related to one another via the gauge/string correspondence. This incredible result, predicted some 30 years ago by 't Hooft and recently presented by Maldacena, shows that a theory of gravity can be described by a theory of nuclear-like interactions! This correspondence is a fascinating bridge between two of the most

一个世纪前，马克斯·普朗克（Max Planck）假定能量不是连续数量，而是它以称为Quanta的离散单位。这些是如此之小，以至于我们通常不会在日常生活中看到它们的影响。但是，它们从根本上改变了理论的特性。在经典理论中，能量和其他数量的这种离散化称为定量。它是针对电磁相互作用以及核力量（统称为量规理论）进行的。这些量子规理论的预测与实验相匹配至壮观的精确度。夸克与其他颗粒（例如电子或质子）不同，因为它们并非出现。它们彼此之间的相互作用如此强烈，以至于单个夸克很快吸引了其他夸克以形成观察到的颗粒，例如质子或中子。这种被称为限制的特性是由于核相互作用的强度或非扰动性的。目前，我们无法源自核互动的量规理论。这是当今理论物理学的最大挑战之一。在普朗克发现的二十年后，爱因斯坦（Einstein）提出了一种称为一般相对论（GR）的重力理论，该理论概括了牛顿的重力定律。在GR时，时空是通过物质弯曲的，例如地球，正是这种曲率使物体在重力下“落”。在许多实验中，GR也已得到验证。然而，GR是一种经典理论，能量是连续数量。启动了量化计理论的成功，物理学家试图量化GR。事实证明，通常的定量过程不能应用于GR！但是能量是物理学的普遍数量。不可能是，物理世界的某些部分（例如原子）是通过量化能量的理论来描述的，而其他描述行星和恒星的理论则由能量连续的理论描述！定量重力的问题已成为物理学中的中心理论问题之一。一种量化重力的替代方法是使用弦理论。在这种方法中，自然的基本颗粒（例如电子，夸克或重力群）根本不是颗粒，而是弦。迄今为止，我们还没有观察到这些字符串，因为它们确实很小。到目前为止，对字符串理论的接受源于理论上的事实，即它们给出了一致的量子计和重力理论。实际上，这两个显然非常不同的是量化重力和解释限制的问题，通过仪表/字符串的对应关系相互关联。大约30年前，这一令人难以置信的结果由'T Hooft预测，最近由Maldacena提出，表明重力理论可以通过类似核样的相互作用理论来描述！这种对应关系是现代理论物理学中两个最具挑战性的问题之间的引人入胜的桥梁。我相信，这种对应关系可以一方面关于仪表理论中的禁闭性质，以及另一方面的重力定量。特别是，我打算找出重力理论如何将自己重新安排为仪表相互作用的理论。通过这样做，我将特别关注重力理论的“严格”本质。最初，我的工作将集中于比核相互作用理论更对称的仪表理论。尽管更像是对称性，但这些理论与现实世界中的理论具有许多相似之处。自从我建议理解这种重新安排的过程以来，这并不明确依赖于量规理论中存在的额外对称性，我期望对这些理论进行大量了解的理论，一旦对量表的理解进行理解的理解，即对衡量理论的理解，以使其更加对称性理论，以使其更加对称，我将其更加融合，以使其对衡量的理论，我将其更加融合，我将其构成对称性的依据，我将其构成对衡量理论，而是将其更加融合。互动。我认为，找出“严格的”重力理论如何将自己重新组织为这些现实的仪表理论，它将教会我们有关非扰动仪表理论的动态，例如限制。这些是如此之小，以至于我们通常不会在日常生活中看到它们的影响。但是，它们从根本上改变了理论的特性。在经典理论中，能量和其他数量的这种离散化称为定量。它是针对电磁相互作用以及核力量（统称为量规理论）进行的。这些量子规理论的预测与实验相匹配至壮观的精确度。夸克与其他颗粒（例如电子或质子）不同，因为它们并非出现。它们彼此之间的相互作用如此强烈，以至于单个夸克很快吸引了其他夸克以形成观察到的颗粒，例如质子或中子。这种被称为限制的特性是由于核相互作用的强度或非扰动性的。目前，我们无法源自核互动的量规理论。这是当今理论物理学的最大挑战之一。在普朗克发现的二十年后，爱因斯坦（Einstein）提出了一种称为一般相对论（GR）的重力理论，该理论概括了牛顿的重力定律。在GR时，时空是通过物质弯曲的，例如地球，正是这种曲率使物体在重力下“落”。在许多实验中，GR也已得到验证。然而，GR是一种经典理论，能量是连续数量。启动了量化计理论的成功，物理学家试图量化GR。事实证明，通常的定量过程不能应用于GR！但是能量是物理学的普遍数量。不可能是，物理世界的某些部分（例如原子）是通过量化能量的理论来描述的，而其他描述行星和恒星的理论则由能量连续的理论描述！定量重力的问题已成为物理学中的中心理论问题之一。一种量化重力的替代方法是使用弦理论。在这种方法中，自然的基本颗粒（例如电子，夸克或重力群）根本不是颗粒，而是弦。迄今为止，我们还没有观察到这些字符串，因为它们确实很小。到目前为止，对字符串理论的接受源于理论上的事实，即它们给出了一致的量子计和重力理论。实际上，这两个显然非常不同的是量化重力和解释限制的问题，通过仪表/字符串的对应关系相互关联。大约30年前，这一令人难以置信的结果由'T Hooft预测，最近由Maldacena提出，表明重力理论可以通过类似核样的相互作用理论来描述！这种对应关系是最引人入胜的桥