Nonperturbative Quantum Fields and Strings

量子场论（QFT）证明了物理学原理的力量。它是融合科学中两个最基本和最具变革性的原则的必然框架：量子力学和相对论。正因为如此，QFT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。描述粒子物理标准模型的量子场论的预言已经被大型强子对撞机上希格斯玻色子的发现所证实。此外，最近来自普朗克卫星的数据加强了解释宇宙大尺度结构起源的图片，因为量子场的波动是种子。这些都是QFT历史上无与伦比的胜利。尽管如此，我们对强耦合区域中的QFT的理解，在那里教科书微扰技术崩溃，是非常不完整的。我的研究项目将调查强耦合系统可以表现出的物理特性。我们的策略是使用我帮助开发的工具来研究QFT，这些QFT表现出丰富的现象，具有足够的对称性，即使在强耦合状态下，也可以对动态进行详尽的理解。其目的是获得理论耦合常数的精确函数公式，从而为物理学家提供一个进入非微扰物理学的宝贵窗口。一个相关的理论和实验挑战是表征在桌面实验中，在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物质的所有可能状态/相。我们的目标是识别和计算QFT和晶格哈密顿中的新观测量，称为序参数，它们可以区分量子系统可能支持的不同相位。识别区分不同相位的新观测量是预测自然界中迄今未知物质状态的重要理论工具。全息原理使我们对弦和M理论的理解发生了转变，由于所谓的AdS/QFT对应，这是我们走向宇宙统一量子理论的最有希望的途径。这种对应关系将反德西特空间（AdS）中的非引力QFT与弦/M理论联系起来。然而，我们无法理解AdS中超越点粒子近似的弦理论，这使得使用AdS/QFT对应来计算量子色动力学等约束规范理论中的强耦合现象变得无效。这就需要在强耦合区的弯曲几何中驯服弦理论的物理。我们建议在AdS中进行弦理论的第一次精确计算。这些将捕获对弦理论的点粒子近似的所有修正。我们将研究弦振幅与适当的边界条件，允许一个精确的评价费曼的路径积分弦世界单理论的局部化功能的积分。解决这个问题的时机已经成熟。在计算这些特殊振幅的过程中所获得的见解，将为弦理论在弯曲时空中是什么提供新的前景。在非微扰机制中理解物理学可以找到许多应用，为我们提供了一个操纵强相互作用系统的新框架，这可能会导致新的技术和材料，以及构建量子计算机的环境。反过来，发现表征新相的算子可以激励实验产生这些新的物质量子态，并带来不可预见的技术副产品。

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.