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 openaccess
resources for the scientific community, which will greatly facilitate further studies of holographic theories.