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

这个研究项目是关于量子场论、弦理论和量子引力，大大加强了对我们物理宇宙的理论理解。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(关联玻色和费米基本粒子)量子场论的新精确结果，以及对六维最大超共形(2，0)理论的新见解。(保角不变性是比例不变性的推广，只要求对应曲线之间的角度不变。)另一个是关于发现规范/引力对应的非微扰粒子相互作用的新的具体例子和含义，以及研究反德西特/共形场理论(ADS/CFT)空间中整体局域性的出现。最后，它将尝试在其他背景下阐述量子引力的精确理论，例如膨胀的德西特宇宙。在发现可以在超对称理论中精确计算的量方面已经取得了重大进展，还有许多有待探索的地方。关键是找到保持超对称性的新背景，然后应用局部化技术将路径积分精确化为有限维积分。这些方法为了解(2，0)理论的结构提供了一个窗口，使其进一步阐明变得可能。这项研究涉及到量子纠缠熵，它给出了量子场论中的单调尺度函数，并探索了ADS/CFT中出现的体积的几何结构。非定域量如球配分函数和纠缠熵控制重整化群在奇数维流动，这意味着拓扑自由度和传播自由度以一种新的方式结合在一起。这个项目的一个方向是寻找这种行为的例子以及对重整化群流的新的一般约束。智力价值：理论量子场论中最重要的开放问题之一是确定它们在强耦合下的动力学。超对称理论的新精确结果将带来对这类系统的新见解。它还对ADS/CFT和其他二元性进行了新的检查。对约束三维重整化群流的自由度数量等量的进一步探索，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。在这一背景下，纠缠熵一直扮演着一个有趣的角色，进一步研究它们的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的理解的新进展。找到与体相对应的共形场理论(CFT)算符的一般特征，即在任意量子态下的可观测性，将对量子引力具有重要的意义。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，并进一步理解涉及最简单的共形场论的对偶性如何适用于弦理论，将提供一个了解规范/引力对应的基本结构的窗口。在德西特空间理解量子引力理论的问题上取得的进展，将揭示这个与我们自己膨胀的宇宙相关的深层次问题。更广泛的影响：这项研究允许参与波士顿地区理论网计划，在高中课堂上进行一年两次的演讲。这是一个很好的方式，可以激发人们发现新的物理基本定律的热情，也可以让人们认识到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、量子引力和高能理论有着跨学科的联系。纠缠熵这门学科是一门很棒的专题研究生课程。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找到新的准确结果，为研究生和博士后提供了极好的可操作性和新颖性的研究项目。

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.