Bootstrability · Solving holographic CFTs through the synergy of integrability and conformal bootstrap.

This proposal will develop innovative methods to access for the first time at non perturbative level the conformal field theory data of the two holographic conformal field theories that provides the best-established paradigms of the AdS/CFT correspondence: N=4 Supersymmetric Yang-Mills (SYM) and ABJM. This goal can be obtained combining the techniques of the conformal bootstrap, both in its analytical and numerical approaches, with integrability. Such methods proved to be very efficient when applied by themselves, and their complementary usage is the main novelty of this project. Considering that integrability provides a set of conformal data (the scaling dimensions), the plan is to use this piece of information as an input for the conformal bootstrap to compute the remaining set of data (structure constants).A strongly interdisciplinary approach, combining analytical and numerical conformal bootstrap together with the most advanced integrability methods, will be adopted to overcome the existing difficulties and compute those quantities. This will be possible thanks to the critical convergence of the expertise of the two supervising mentors and the researcher on different aspects of bootstrap and integrability. A crucial role will be played by novel techniques developed in recent years by the researcher. The new methods resulting from this action are expected to have a wide applicability, allowing the study of general correlation functions and to lead to quantitative answers to outstanding questions on AdS/CFT. The training plan is designed to boost significantly the researcher's scientific skills, as well as his teaching abilities with the delivery of two PhD level courses. The action involves a strong dissemination and outreach plan including scientific divulgation, a public lecture and the creation of a website/repository hosting permanent open-access resources for the scientific community, which will greatly facilitate further studies of holographic theories.