Gauge Theories and String Theory Dynamics

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的许多现象，包括高能物理、宇宙学和凝聚态物理。它甚至对数学产生了深刻的影响。在大型强子对撞机上发现了希格斯玻色子，这极大地证实了量子理论中描述粒子物理标准模型的预言。此外，来自普朗克卫星的数据也加强了解释宇宙大尺度结构起源的图像，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。尽管取得了这些突破，但我们对量子效应非常大的非微扰区的量子理论的理解还很不完整。 我的研究项目是研究非微扰系统可能表现出的物理性质和现象。总的来说，这些系统仍未被探索。这包括使用最近出现的新想法和技术，这些新想法和技术首次允许回答QFT中与粒子物理、凝聚态物理甚至数学直接相关的长期存在的问题。我的团队的目标是解决QFT的低能非微扰动力学问题。这些问题的答案可能导致对物质的新量子状态的预测，例如拓扑超导体，以及不可预见的技术副产品。 弦理论是量子引力理论的主要候选者，它将粒子物理学的基本力与引力统一起来。它融合了由量子力学支配的最小距离的物理学和由引力支配的最远距离的物理学。这导致了对近距离时空和物质结构的丰富洞察。 这一提议的一个中心目标是为我们最近构建并被称为非相对论弦理论的一种新型弦理论发展物理基础，该理论基于新的对称性和原理。这个弦理论描述了弦在一种新的弯曲时空几何上的传播和相互作用，这种几何不同于广义相对论的基础几何。我和我的HQP团队的目标是探索和发展新的低能引力理论的物理和数学性质，以及从这个新的弦理论中出现的低能QFT。这些理论的对称性可以出现在各种量子多体系统中，在这些系统中，可以实现不同的对称性，包括非相对论对称性。这可能导致一种新的框架来操纵强耦合系统并对其进行建模，从而产生新的材料和技术。

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. It has even deeply impacted mathematics. 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. Also, 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 breakthroughs, our understanding of QFT in the nonperturbative regime, where quantum effects are very large- is very far from complete. My research program investigates the physical properties and phenomena that nonperturbative systems can exhibit. These systems have by in large remained unexplored. This includes the use of new ideas and techniques that have recently become available and that allow to answer, for the first time, long standing questions in QFT, directly relevant to particle physics, condensed matter physics and even mathematics. My team's objective is to solve for the low energy nonperturbative dynamics of QFTs. The answer to these questions can lead to the prediction of new quantum states of matter, such as topological superconductors, with unforeseen technological spinoffs. String theory is the leading candidate for a theory of quantum gravity and unifies the fundamental forces of particle physics with gravity. It merges the physics at the smallest distances, governed by quantum mechanics, with the physics at the largest distances, governed by gravity. This has led to a wealth of insights about the structure of spacetime and matter at short distances. A central aim of this proposal is to develop the physical foundations of a new type of string theory we have recently constructed and dubbed by Nonrelativistic String Theory, which is based on novel symmetries and principles. This string theory describes the propagation and interactions of strings on a new type of curved spacetime geometry that is distinct from the geometry underlying General Relativity. My team of HQPs and I aim to explore and develop the physical and mathematical properties of the new low energy gravitational theory and QFTs emerging at low energies from this new string theory. These theories have symmetries that can appear in various quantum many body systems, where distinct symmetries, including nonrelativistic symmetries, can be realized. This could lead to a new framework to manipulate and model strongly coupled systems, leading to novel materials and technologies.