Nonperturbative Gauge Theory

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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.