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

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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.