The publications develop the Researcher's Physical Review Letters paper at the base of the Fellowship. Systems that possess an infinite number of conserved charges are called integrable. The correlators of operators, which encode physical information, can be solved exactly (a rare fact in the quantum world) and subtend many finite-coupling results. A milestone for correlators of 2 operators is a well-studied system of equations, called quantum spectral curve, while for 3 another (hexagon) framework is in place. The Researcher's paper made a framework for baryonic-like operators.
The Publication 1 concerned the correlators of 4 baryons. They harbour interesting physics (from string-theory tachyons to boundary states). The Researcher made the preliminary steps by collecting small-coupling data. Comments were made on the phase transition that such correlator is expected to exhibit in an integrability-based framework.
The Publication 2 initiated the study of baryons in fishnet models. Our motivation stemmed from the growing evidence that the Separation of Variables method (based on the quantum spectral curve) may apply to this type of correlators too. Such re-formulation would ultimately contribute to develop universal computational methods based on integrability. The Researcher revisited baryons (quantum properties, Feynman diagrams, resummation) and qualitatively examined a great variety of correlators, identifying those solvable by operatorial/integrability methods. What is also important is the set of future directions: other "heavy" operators, the search for integrable boundary states, other fishnets with integrable sectors and the study of branes in the gauge/string correspondence.
The work in preparation is about loop equations, which are tools to study quantum field theories in 0 dimensions, or matrix models. In supersymmetric Yang-Mills theory, one matrix integral measures a certain (half-BPS, circular) Wilson loop. This opens a unique avenue in quantum models, where physical informations is a very complicated integral (in infinite dimensions, not zero). For some (Hermitian, beta-ensembles) matrix models, recursive (topological) solutions have been developed, but are virtually confined to the simplest models. The Researcher considered a general class, formulated the loop equation and an algorithm to construct the solution to arbitrary order in genus expansion. We put forward new high-precision small/large-coupling coefficients and perform a numerical study at intermediate coupling. Important applications are a massive version of supersymmetric Yang-Mills theory and the Hoppe model. The loop equation is the tool to move the goalpost to the finite-coupling range, probes similar supersymmetric theories and supports string theory and integrability studies.
