Nonperturbative Quantum Fields and Strings

量子场论(QFT)体现了原理在物理学中的力量。这是一个必然的框架，融合了科学中两个最基本和最具变革性的原理：量子力学和相对论。正因为如此，量子傅立叶变换是所有现代物理学的核心。它以前所未有的成功描述了自然界中的许多现象，包括高能物理、宇宙学和凝聚态物理。量子力学描述粒子物理标准模型的预言已经被大型强子对撞机上发现的希格斯玻色子壮观地证实了。此外，来自普朗克卫星的最新数据加强了解释宇宙大尺度结构起源的图景，因为宇宙的大尺度结构是由量子场的波动播种的。这些都是QFT历史上无与伦比的胜利。尽管如此，我们对强耦合区域的量子理论的理解还远远没有完成，在强耦合区域，教科书中的微扰技术崩溃了。我的研究计划将调查强耦合系统可能表现出的物理性质。我们的策略是使用我帮助开发的工具来研究QFT，这些QFT表现出足够对称的丰富现象，即使在强耦合状态下也能对动力学有一个详尽的理解。目标是得到理论耦合常数的精确函数的公式，从而为物理学家提供了解非微扰物理的宝贵窗口。一个相关的理论和实验挑战是表征在桌面实验、早期宇宙和粒子加速器中，特别是在强耦合系统中可能形成的所有物质的状态/相。我们的目标是在量子傅里叶变换和晶格哈密顿量中识别和计算新的可观测到的，称为序参数，它们区分量子系统可能支持的不同相位。识别区分不同相的新的可观测值是预测自然界中迄今未知的物质状态的重要理论工具。全息原理导致了我们对弦和M理论的理解的转变，这是我们通向宇宙统一量子理论的最有希望的方法，这要归功于所谓的ADS/QFT对应。这种对应在反de-Sitter空间(ADS)中用弦/M理论证明了一种非引力QFT。然而，我们无法超越点粒子近似来理解ADS中的弦理论，这使得我们无法使用ADS/QFT对应来计算像量子色动力学这样的约束规范理论中的强耦合现象。这需要在强耦合方案中驯服弯曲几何中的弦理论物理。我们建议在ADS中执行弦理论的第一个精确计算。这些将捕捉到对弦理论的点粒子近似的所有修正。我们将研究具有适当边界条件的弦振幅，以允许通过泛函积分的局部化来精确地计算弦世界表理论上的费曼路径积分。解决这个问题的时机已经成熟。从这些特殊振幅的计算中获得的见解将为弦理论在弯曲时空中的应用提供新的视角。理解非微扰状态下的物理学可以找到许多应用，给我们一个操作强相互作用系统的新框架，这可能导致新的技术和材料，以及一个建立量子计算机的环境。表征新相的运算符的发现反过来可以推动实验，以产生这些新的物质量子状态，并产生意想不到的技术副产品。

Quantum Field Theory (QFT) exemplifies the power of principles in physics. It is the inevitable framework merging two of the most fundamental and transformative principles in science: Quantum Mechanics and Relativity. Because of this, QFT is at the heart of all modern physics. It describes, with unprecedented success, many phenomena in nature, including in high energy physics, cosmology and condensed matter physics.The predictions of QFT describing the Standard Model of Particle Physics have been spectacularly confirmed by the discovery of the Higgs boson at the Large Hadron Collider. Further, recent data from the Planck satellite have strengthened the picture explaining the origin of the large scale structure of the Universe as being seeded by fluctuations of a quantum field. These are unparalleled triumphs in the history of QFT. Despite these, our understanding of QFT in the strong coupling regime, where textbook perturbative techniques breakdown, is very far from complete.My research program will investigate the physical properties that systems that are strongly coupled can exhibit. The strategy is to use tools that I have helped develop to study QFTs exhibiting rich phenomena with enough symmetry to allow an exhaustive understanding of the dynamics even in the strong coupling regime. The objective is to obtain formulas that are exact functions of the coupling constant of the theory, thus giving physicists a precious window into nonperturbative physics.A related theoretical and experimental challenge is to characterize all the possible states/phases of matter that can be formed in tabletop experiments, in the early universe and in particle accelerators, specially in strongly coupled systems. We aim to identify and compute new observables in QFTs and lattice Hamiltonians, known as order parameters, that distinguish the different phases that a quantum system may support. Identifying new observables that distinguish the different phases is an important theoretical tool for predicting hitherto unknown states of matter in Nature.The Holographic Principle has resulted in a transformation of our understanding of string and M- theory, which is our most promising approach towards a unified quantum theory of the universe, thanks to the so-called AdS/QFT correspondence. This correspondence identifies a non-gravitational QFT with string/M-theory in Anti-de-Sitter space (AdS). However, our inability to understand string theory in AdS beyond the point particle approximation, invalidates the use of the AdS/QFT correspondence to compute strongly coupled phenomena in confining gauge theories like Quantum Chromodynamics. This requires taming the physics of string theory in curved geometries in the strong coupling regime.We propose to perform the first exact computations of string theory in AdS. These will capture all corrections to the point particle approximation to string theory. We will study string amplitudes with suitable boundary conditions that allow an exact evaluation of the Feynman's path integral on the string worldsheet theory by localization of the functional integral. The time is ripe to tackle this problem. The insights obtained in the computation of these special amplitudes will provide new vistas on what string theory is in curved spacetimes.Understanding physics in the nonperturbative regime can find many applications, giving us a new framework to manipulate strongly interacting systems, which may result in new technologies and materials, and an environment on which to build a Quantum Computer. The discovery of operators characterizing new phases, in turn, can motivate experiments to produce these new new quantum states of matter, with unforeseen technological spinoffs.