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

共形场理论(CFT)是一种现代理论框架，它允许我们对从物质相到量子引力的各种物理现象进行推理。CFT最重要的例子是极其复杂、强耦合的系统。理论物理学中的一大挑战是为这类系统开发有效的工具。共形自举是近年来出现的一种非常成功和普遍的方法。然而，有许多重要的CFT，例如它的共形窗口中的量子色动力学，或者违反统一性的CFT，这些目前是遥不可及的。此外，我们不知道在一般CFT的光谱中是否存在通用结构，或者我们认为存在的结构实际上在多大程度上存在。CFTSPEC将利用共形自举内外的新技术来解决这些问题，并极大地扩展我们对CFT的理解。它将结合数值和分析、微扰和非微扰方法来约束和分类CFT，并获得对其基本性质的新见解。在数值方面，CFTSPEC将使用新的数值引导技术来访问鲜为人知的CFT。在分析方面，CFTSPEC将通过与散射幅度的红外发散建立新的联系，以及通过与数值方法和更传统的分析方法的相互作用，来开发详细的光线操作符理论。CFTSPEC的结果将包括实验相关CFT的精确数值结果，对所有CFT空间的普遍限制，以及在理解它们的基本性质和谱方面的重大进展。CFTSPEC结合了几种非常不同的方法来研究共形场理论。我在所有这些项目中的专业知识和记录使我处于领导这个项目的独特位置，并交付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.