Nonperturbative Gauge Theory

我研究量子场论（QFT）的动力学。QFT是用来描述基本粒子物理学以及多体凝聚态系统物理学的理论框架。一般qft的动力学可能非常复杂，并且仍然没有被理解。它包含了与强强子相互作用相关的约束和手性对称破缺等现象。更一般的qft可以有不同的相，比如共形相，或者它们可以打破它们的对称性并产生不同的质量尺度。更好地理解量子场效应的可能相位是相关的，例如，对于超越标准模型的物理模型来说——不同于标准模型的量子场效应可能是希格斯粒子神秘特性的原因，或者与解释令人费解的自然质量等级有关。这种qft的表现可能在大型强子对撞机（LHC）、未来的粒子加速器或宇宙学观测的实验范围内。此外，正如最近在qft形式化方面的发展所表明的那样，过去已经忽略了qft的重要性质，特别是存在新颖的t Hooft异常匹配条件。我目前的研究在很大程度上是出于对理论的好奇心，目的是发现有趣的，以前不被理解的，一般qft的动力学和可能阶段的方面。为了研究QFT的非微扰动力学，我使用了不同工具的组合，包括半经典方法、超对称、晶格场理论、新旧发现的一致性条件的应用，偶尔还使用弦理论和D膜。提出的非微扰规范动力学的研究将进一步加深我们对规范理论动力学的理论认识。在过去，使用的方法对量子场论的特性产生了重要的见解，这些特性以前被认为是难以解决的。例如，他们发现并阐明了新型“拓扑分子”在约束、共态和热约束跃迁物理中的作用。我希望对诸如约束、解定义和四维规范理论的可能相位等复杂现象有进一步的新见解，并对量子场论的数学结构的更正式的问题有更深入的了解。这些是规范理论中最不为人所知的方面。我的提案的很大一部分致力于研究最近发现的涉及更高形式对称性的UV/IR一致性条件，例如中心对称。这些条件严重限制了许多规范理论的红外相位。他们对理论的理解还处于初级阶段。除了我们和其他机构最近考虑的qft之外，对更广泛的qft的申请也有待考虑。

I study the dynamics of quantum field theory (QFT). QFT is the theoretical framework used to describe the physics of elementary particles as well as the physics of many--body condensed matter systems. The dynamics of general QFTs can be very complex and is still ill understood. It encompasses such phenomena as confinement and chiral symmetry breaking, relevant for the strong hadronic interactions. More general QFTs can have different phases, such as conformal phases, or they can break their symmetries and generate different mass scales. A better understanding of the possible phases of QFT is relevant, for example, for models of Physics Beyond the Standard Model-QFTs different from those in the Standard Model may be responsible for the mysterious properties of the Higgs particle or be relevant to explaining the puzzling mass hierarchies of nature. The manifestations of such QFTs may be within the experimental reach of the Large Hadron Collider (LHC), of future particle accelerators, or of cosmological observations. Further, as recent developments in formal aspects of QFTs have shown, important properties of QFTs have been missed in the past, notably the existence of novel 't Hooft anomaly matching conditions. My current research is largely motivated by theoretical curiosity and aims to uncover interesting, previously not understood, aspects of the dynamics and possible phases of general QFTs. To study the nonperturbative dynamics of QFT, I use a combination of different tools, including semiclassical methods, supersymmetry, lattice field theory, the application of old and newly discovered consistency conditions, and occasionally, string theory and D--branes. The proposed investigations of nonperturbative gauge dynamics will further our theoretical understanding of the dynamics of gauge theories. The methods used have, in the past, yielded significant insights into properties of quantum field theories previously deemed intractable. For example, they found and elucidated the role of novel "topological molecules" in the physics of confinement, conformality, and the thermal deconfinement transition. I expect to obtain further new insights into such complex phenomena as confinement, deconfinement, and the possible phases of four dimensional gauge theories, as well as insights into more formal questions about the mathematical structure of quantum field theories. These are among the least understood aspects of gauge theories. A large part of my proposal is devoted to a study of the recently discovered UV/IR consistency conditions involving higher--form symmetries, such as center symmetry. These conditions severely constrain the infrared phases of many gauge theories. Their better theoretical understanding is in its infancy. Applications to a wider variety of QFTs, in addition to those considered recently, by us and by others, also await to be considered.