CAREER: Quantum Field Theory in Diverse Dimensions, Supersymmetry, and Quantum Gravity

这个研究计划是关于量子场论，弦理论和量子引力，大大加强了我们的物理宇宙的理论理解。其中一个重点是寻找强相互作用量子场论的新的一般性质，超对称（涉及玻色子和费米子基本粒子）量子场论的新的精确结果，以及对六维最大超共形（2，0）理论的新见解。（共形不变性是尺度不变性的推广，只要求相应曲线之间的角度不改变。另一个是发现新的具体例子和非微扰粒子相互作用的规范/引力对应的影响，并研究出现的反德西特/共形场理论（AdS/CFT）空间的大局部。最后，它将试图制定量子引力在其他背景下的精确理论，如扩展的德西特宇宙。在发现超对称理论中可以精确计算的量方面已经取得了重大进展，还有很多东西有待探索。关键是找到新的背景，其中超对称性是保持，然后应用本地化技术，以获得一个精确的减少的路径积分的有限维积分。这些方法为（2，0）理论的结构提供了一个窗口，使其进一步阐明成为可能。研究涉及量子纠缠熵，给出量子场论中尺度的单调函数，并探讨AdS/CFT中出射体的几何结构。非局部量，如球配分函数和纠缠熵控制重整化群流在奇数维，这意味着拓扑和传播自由度相结合的一种新的方式。这个项目的一个方向是找到这种行为的例子，以及重整化群流的新的一般约束。智力优势：在理论量子场论中最重要的一个未解决的问题是确定它们在强耦合下的动力学。超对称理论的新的精确结果，预计将导致新的洞察这样的系统。它还提供了AdS/CFT和其他二元性的新检查。进一步探索限制三维重正化群流的自由度等量，将导致对凝聚态系统中可能出现的长距离行为的有趣的新预测。纠缠熵在这方面发挥了重要作用，进一步研究其一般性质将带来新的进展。六维最大超共形理论的可计算描述的发现将导致对低维超对称理论理解的新进展。找到与体相对应的共形场论（CFT）算符的一般特征，即任意量子态中的可观测量，将对量子引力产生重要影响。这将是在一般背景下理解量子引力的一步，并将揭示黑洞信息悖论。AdS/CFT的新例子，以及进一步理解包含最简单共形场论的对偶如何适合弦理论，将为了解规范/引力对应的基本结构提供一个窗口。在德西特空间中理解量子引力理论的问题上取得的进展，将使我们对这个与我们自己的膨胀宇宙有关的深层次问题有所了解。更广泛的影响：这项研究允许参与波士顿地区的Theorynet计划，提供一年两次的会谈，高中教室。这是一个很好的方式来传授发现新的物理学基本定律的热情和科学好奇心的重要性。强相互作用量子场论的理论研究也与凝聚态物理学、量子引力和高能理论有着跨学科的联系。纠缠熵是研究生的一门重要的专题课程。它与信息论、凝聚态物理、量子场论和量子引力有关。最后，通过这项研究，在超对称量子场论中发现新的精确结果，为研究生和博士后提供了优秀的可管理但新颖的研究项目。

This research program is about quantum field theory, string theory and quantum gravity, greatly strengthening the thoretical understanding of our physical universe. One focus is on finding new general properties of strongly interacting quantum field theories, new exact results in supersymmetric (relating bosonic and fermionic elementary particles)quantum field theories, and new insights into the maximally superconformal (2,0) theory in six dimensions. (Conformal invariance is a generalization of scale invariance that only requires that the angles between corresponding curves do not change.) Another is on discovering new concrete examples and implications for non-perturbative particle interactions of the gauge/gravity correspondence, and researching the emergence of bulk locality in Anti-de Sitter/Conformal Field Theory (AdS/CFT) space. Lastly, it will attempt to formulate the exact theory of quantum gravity in other backgrounds, such as an expanding de Sitter universe. Major progress has been made in discovering quantities that can be calculated exactly in supersymmetric theories, and much remains to be explored. The keys are finding new kinds of backgrounds in which supersymmetry is preserved, and then applying the technique of localization to obtain an exact reduction of the path integral to a finite dimensional integral. Such methods have given a window into the structure of the (2,0) theory, which puts its further elucidation within possible reach. The research involves the quantum entanglement entropies that give a monotonic function of scale in quantum field theories and probe the geometric structure of the emergent bulk in AdS/CFT. Nonlocal quantities such as the sphere partition function and entanglement entropy control renormalization group flows in odd dimensions implying that topological and propagating degrees of freedom are combined in a novel way. One direction of this project is to find examples of such behavior as well as new general constraints on renormalization group flows. Intellectual Merit : One of the most important open questions in theoretical quantum field theory is the determination of their dynamics at strong coupling. The new exact results for supersymmetric theories that are expected will lead to new insight into such systems. It also gives new checks of AdS/CFT and other dualities. Further explorations of quantities like the number of degrees of freedom that constrain renormalization group flows in three dimensions will lead to interesting new predictions for long distance behavior that may arise in condensed matter systems. Entanglement entropies have been playing an intriguing role in this context, and further exploring their general properties will lead to new advances. The discovery of a calculable description of the maximally superconformal theory in six dimensions will lead to new advances in understanding of supersymmetric theories in lower dimensions. Finding the general characterization, observables in arbitrary quantum states, of conformal field theory (CFT) operators that correspond to bulk will have significant implications for quantum gravity. It will be a step in understanding quantum gravity in general backgrounds, and would shed light on the black hole information paradox. New examples of AdS/CFT, and further understanding how the dualities involving the simplest conformal field theories fit into string theory will provide a window into the basic structure of the gauge/gravity correspondence. Advances in the problem of understanding the theory of quantum gravity in de Sitter space will shed light on this deep question relevant to our own expanding universe. Broader Impacts : This research allows participation in the Boston area Theorynet program, delivering biannual talks to high school classrooms. This is a good way to impart the enthusiasm for discovering new fundamental laws of physics and the importance of scientific curiosity in general. The theoretical research in strongly interacting quantum field theories also has interdisciplinary connections to condensed matter physics, as well as quantum gravity and high energy theory. The subject of entanglement entropy makes a great special topics graduate course. It is relevant to information theory, condensed matter physics, quantum field theory and quantum gravity. Lastly, through this research, finding new exact results in supersymmetric quantum field theories makes excellent manageable yet novel research projects for graduate students and postdocs.