Nonperturbative Gauge Theory

我研究量子场论（QFT）的动力学。量子场论是用来描述基本粒子物理和多体凝聚态系统物理的理论框架。一般QFT的动力学可能非常复杂，并且仍然不太清楚。它包括禁闭和手征对称性破缺等现象，与强强子相互作用有关。更一般的QFT可以具有不同的相，例如共形相，或者它们可以打破其对称性并产生不同的质量尺度。更好地理解QFT的可能阶段是相关的，例如，对于超越标准模型的物理模型，与标准模型不同的QFT可能是希格斯粒子神秘性质的原因，或者与解释自然界令人困惑的质量等级有关。这种QFT的表现可能在大型强子对撞机（LHC）、未来粒子加速器或宇宙学观测的实验范围内。此外，正如QFT形式方面的最新发展所示，QFT的重要性质在过去被忽略了，特别是新的特胡夫特异常匹配条件的存在。我目前的研究主要是出于理论上的好奇心，旨在揭示有趣的，以前不理解的，一般QFT的动态和可能的阶段方面。为了研究QFT的非微扰动力学，我使用了不同的工具，包括半经典方法，超对称性，格场理论，旧的和新发现的一致性条件的应用，偶尔，弦理论和D-膜的组合。对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理解。在过去，所使用的方法对以前被认为是棘手的量子场论的性质产生了重要的见解。例如，他们发现并阐明了新的“拓扑分子”在限制，保形性和热解除限制过渡物理学中的作用。我希望能获得进一步的新见解等复杂的现象，如禁闭，解除禁闭，和可能的阶段的四维规范理论，以及洞察到更正式的问题有关的数学结构的量子场论。这些都是规范理论中最不为人所知的方面。我的建议的很大一部分是致力于最近发现的UV/IR一致性条件的研究，涉及更高形式的对称性，如中心对称性。这些条件严格限制了许多规范理论的红外相位。他们更好的理论理解还处于起步阶段。除了我们和其他人最近考虑的那些申请外，更多种类的QFT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.