CFTSPEC: Spectra of Conformal Theories: From Trajectories, Colliders, and Numerics

共形场论（Conformal Field Theory，CFT）是一个现代的理论框架，它允许我们推理各种各样的物理现象，从物质的相到量子引力。最重要的例子是非常复杂的强耦合系统。理论物理学的一个巨大挑战是为这样的系统开发有效的工具。保形引导是近年来出现的一种非常成功和通用的方法。然而，有许多重要的连续泛函理论，例如在共形窗口中的量子色动力学，或者违反么正性的连续泛函理论，目前还无法实现。此外，我们不知道在一般的连续泛函理论的谱中是否存在一个普适的结构，或者在多大程度上我们认为存在的结构实际上存在。CFTSPEC将利用共形引导和超越的新技术来解决这些问题，并大大扩展我们对CFTs的理解。它将结合联合收割机的数值和分析，微扰和非微扰的方法来约束和分类的CFTs，并获得新的见解，他们的基本属性。在数值方面，CFTSPEC将使用新的数值引导技术来访问理解不足的CFTs。在分析方面，CFTSPEC将通过与散射振幅的红外发散的新联系，以及通过与数值和更传统的分析方法的相互作用，开发光线算子的详细理论。CFTSPEC的成果将包括精确的数值计算结果的实验相关的CFTs，所有CFTs的空间上的普遍约束，以及在理解其基本属性和spectrum.CFTSPEC结合了几个非常不同的方法共形场理论的重大进展。我在所有这些方面的专业知识和业绩记录使我处于一个独特的位置来领导这个项目，并提供CFTSPEC设想的开创性成果。

Conformal Field Theory (CFT) is a modern theoretical framework which allows us to reason about an extremely wide variety of physical phenomena, ranging from phases of matter to quantum gravity. Most important examples of CFTs are extremely complex, strongly-coupled systems. One of the great challenges in theoretical physics is developing efficient tools for such systems. The Conformal Bootstrap emerged in recent years as an extremely successful and general approach. Yet, there are many important CFTs, for example Quantum Chromodynamics in its conformal window, or CFTs that violate unitarity, which are currently out of reach.Furthermore, we do not know if there is a universal structure in the spectrum of general CFTs, or to what extent the structures that wesuspect to exist actually do. CFTSPEC will utilize new techniques within the conformal bootstrap and beyond to address these questions and greatly expand our understanding of CFTs. It will combine numerical and analytical, perturbative and non-perturbative approaches to constrain and classify CFTs, and to gain new insight into their fundamental properties. On the numerical side, CFTSPEC will use novel numerical bootstrap techniques to access poorly-understood CFTs. On the analytical side, CFTSPEC will develop a detailed theory of light-ray operators, both through a new connection to infrared divergences of scattering amplitudes, as well as through the interplay with numerical and more traditional analytic methods. The outcomes of CFTSPEC will include precise numerical results for experimentally relevant CFTs, universal constraints on the space of all CFTs, as well as a major advance in the understanding of their fundamental properties and spectra.CFTSPEC combines several very distinct approaches to conformal field theory. My expertise and track record in all of them place me in a unique position to lead this project and to deliver the groundbreaking results that CFTSPEC envisions.