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Supergravity and field theory solutions in AdS/CFT correspondence

AdS/CFT 对应中的超重力和场论解决方案

基本信息

批准号：
EP/G050015/1
负责人：
Aristomenis Donos
金额：
$ 31.31万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2009
资助国家：
英国
起止时间：
2009 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FG050015%2F1
关键词：
Supergravity field theory solutions AdS

项目摘要

Modern theoretical physics has made big steps in addressing longstanding, fundamental questions. Problems like the confinement of quarks in QCD, the black hole information paradox, the cosmological constant problem and dark matter are now looking for answers in a single, unified theory, string theory.The most recent, and also one of the most promising, development in approaching a set of these issues is the AdS/CFT conjecture. This conjecture relates superconformal field theories to string theory or M-theory defined on spacetimes which are products of Anti de Sitter space, of one dimension higher than the corresponding super conformal field theory is defined on, times a compact space summing up to a total number of ten or eleven dimensions. One of the most interesting aspects, and also one of the main difficulties proving the conjecture, is that it is a weak-strong coupling correspondence.Conformal field theories defined on spacetimes of various dimensions provide us with a viable description of interesting phenomena like critical phenomena, phase transitions, renormalization group flows describing where massive quantum field theories flow to under the renormalization group. The range of areas that conformal field theories have been proved to be of primary interest is vast, varying from the Quantum Hall Effect to Network Models relevant in economics studies.In order to actually take advantage of the conformal field theoretical description one should be able to perform calculations, in particular the correlation functions, at all regimes of the various coupling constants that appear. In general, the systematics of perturbation theory is applicable only in the weak coupling regime of any field theory whereas interesting phenomena, like the QCD confinement, happen at the strong coupling regime which is inaccessible with the standard perturbative techniques and methodology. On the other side of the duality, the weak coupling description of the corresponding string theory is, in principle, tractable and perturbation theory can be employed to extract quantitative answers from it. The AdS/CFT correspondence provides us with an invaluable tool in studying strongly coupled conformal field theories.The AdS/CFT conjecture has not been proved at full generality yet and the collection of evidence that would lead to proving, or disproving it, is rather crucial at this stage. My research will partially focus in various non-trivial investigations on both sides of the correspondence for which the dictionary of the conjecture suggests that we have a different description of the same physical system. One of the examples that I want to consider is the study supergravity dual of supersymmetric Wilson loop operators present in superconformal gauge theories as N=4 super Yang-Mills theory in four spacetime dimensions. These operators have been extensively studied and various properties of them have been investigated. Since AdS/CFT predicts that every operator should have a string theory dual, it is rather crucial to prove that a string theory description of them exists and that it predicts exactly the same properties with the ones that have been discovered from field theory considerations.The second part of my research will focus on the ongoing program of classification of superconformal field theories that have a string theory description.In general, conformal invariance of string theory requires that the backgrounds used to study the theory on should be solutions of the corresponding low energy limit, a supergravity theory. A special class of such backgrounds would be the ones relevant for AdS/CFT, namely backgrounds that contain a global Anti de Sitter factor in the geometry. The question then reduces to describing which compact spaces are allowed to be the second factor of the product space.

现代理论物理学在解决长期存在的基本问题方面取得了重大进展。QCD中的夸克禁闭、黑洞信息悖论、宇宙学常数问题和暗物质等问题现在都在一个统一的理论--弦理论中寻找答案。最近，也是最有希望的一个发展是AdS/CFT猜想。这个猜想将超共形场论与定义在时空上的弦理论或M-理论联系起来，时空是Anti de Sitter空间的乘积，比相应的超共形场论定义在，乘以一个总共有10或11维的紧致空间。其中最有趣的一点，也是证明该猜想的主要困难之一，是它是一个弱-强耦合对应。定义在不同维时空上的共形场论为我们提供了一个可行的描述有趣的现象，如临界现象，相变，重正化群流描述重正化群下的大质量量子场论流。共形场论的研究领域非常广泛，从量子霍尔效应到与经济学相关的网络模型。为了真正利用共形场论的描述，人们应该能够在各种耦合常数的所有状态下进行计算，特别是相关函数。一般来说，微扰论的系统学只适用于任何场论的弱耦合区域，而有趣的现象，如QCD禁闭，发生在强耦合区域，这是用标准微扰技术和方法无法达到的。在对偶性的另一面，弦理论的弱耦合描述在原则上是容易处理的，微扰论可以从中提取定量的答案。AdS/CFT对应为我们研究强耦合共形场论提供了一个非常宝贵的工具。AdS/CFT猜想还没有被完全普遍地证明，收集证据将导致证明，或者反驳它在这个阶段是相当关键的。我的研究将部分集中在各种非平凡的调查双方的对应关系，其中的字典的猜想表明，我们有一个不同的描述相同的物理系统。我想考虑的例子之一是研究超对称威尔逊回路算子的超引力对偶，这些算子存在于超共形规范理论中，作为四维时空中N=4的超杨-米尔斯理论。这些算子已被广泛研究，并研究了它们的各种性质。由于AdS/CFT预言每个算子都应该有一个弦理论对偶，因此证明它们的弦理论描述存在，并且它预言的性质与从场论考虑中发现的性质完全相同是相当关键的。我研究的第二部分将集中在正在进行的具有弦理论描述的超共形场论的分类计划上。一般来说，弦理论的共形不变性要求用来研究理论的背景应该是相应的低能极限，即超引力理论的解。一类特殊的背景是与AdS/CFT相关的背景，即在几何结构中包含全局Anti de Sitter因子的背景。这个问题然后减少到描述哪些紧空间被允许作为产品空间的第二个因素。