The progress beyond the state of the art has been reported so far in two directions: towards the Lagrangian formulation of HS Gravity in d=3 and d=4.
For d=3, the full classification of the interactions involving massless HS fields was completed in 2019. Building on these results, the construction of Lagrangian theories for HS Gravity with a matter in d=3 is a work in progress currently.
In d=4, the macroscopic spacetime dimension of our real world, the standard formulation of massless fields of any spin, the so-called Fronsdal formulation, is not able to capture all the interactions of massless HS fields. Therefore, one needs a new formulation of massless dynamics. In 2019, I started a program of deriving a new
formulation of massless dynamics, treating electric and magnetic degrees of freedom on an equal footing. We already developed such a formulation for spin one making remarkable progress in this century-old subject. We managed to develop a new formulation where the Lorentz invariant Lagrangian is given for the democratic
description of arbitrary non-linear electrodynamics theory and further extend these results to higher-dimensional p-form generalizations. The results of our research were published in highly-ranked scientific journals. In particular, we published a paper in Phys. Rev. Lett., in 2021 with Zhirayr Avetisyan and Oleg Evnin. The development
of this democratic approach to spin two and higher spins is a work in progress. Such a formulation will define a new description with more symmetries for arbitrary massless degrees of freedom in 3+1 dimensions, thus allowing us to address the problem of the nonlinear Lagrangian for Vasiliev's theory from a new perspective.
The results of this project comprise several important steps toward our goal: constructing the simplest complete example of Quantum Gravity. Reaching this goal can spark excitement in the high-energy physics community and lead to the fast development of many new methods relevant to address different issues in particle
physics, gravitational waves, and related areas, finally leading to experiments probing quantum properties of gravity in the real world. The research program started during the project will lead to further high-impact publications over several years to come in addition to the reported publications during the project period.
To conclude, this project has served its purpose making drastic progress toward its final research goals and supporting the professional development of the individual researcher.
