Baryonic operators in conformal field theories
The current theoretical description of the fundamental constituents of matter is the Standard Model of particle physics. Despite the unprecedented experimental verification, most of its predictive power is limited to the regime where particles interact weakly, hence impeding the study of bound states, such as baryons, where interactions are strong.  This proposal aims to study suitable generalizations of these particle excitations – ""baryonic"" operators composed of a number N of fundamental fields at a common point in spacetime – in quantum field theories that possess conformal symmetry and admit a large-N limit. These conditions are essential for the methods used in this proposal, which are based on quantum integrability of the relevant theory and on techniques for analytic resummation of Feynman diagrams.  The proposed research will extend in a non-trivial way the recent progress in solving correlation functions at finite coupling in maximally supersymmetric Yang-Mills theory. Specifically, we plan to advance the state of the art of integrability, in the form of the Quantum Spectral Curve formalism originally designed for two-point correlators, to describe a class of three-point correlators involving baryonic (also known as determinant or giant-graviton) operators.  We also strive to achieve a finite-coupling description of baryonic correlators through an appropriate diagrammatical methodology. Specifically, we plan to realize this goal in the non-supersymmetric gamma-deformation of the Yang-Mills theory and, finally, to adapt it to the quantum mechanical model proposed by Sachdev, Ye and Kitaev. The complicated perturbative description of baryons is both the challenge and the novelty, compared to earlier works for single-trace operators in the same theories.  This proposal details a plan for dissemination and communication of its results to specialists and the general public, as well as training for the benefit of the experienced researcher.