Holography, Ensembles, and Quantum Gravity

This award funds the research activities of Professor Anatoly Dymarsky at the University of Kentucky. Reconciling quantum mechanics with Einstein's theory of gravity, also known as the general theory of relativity, is one of the central open problems in physics. Under this grant award, Professor Dymarsky will construct and analyze exactly solvable models of quantum gravity in three spacetime dimensions, one dimension less than the world we live in. The reduced dimension will simplify the problem and make it tractable. The project is closely connected to Quantum Information Science, as error-correcting codes, a key mathematical ingredient of quantum computing technologies, play a prominent role in the research. As a result, research in this area advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical law. It will also have significant broader impacts: Professor Dymarsky will train graduate students, develop a graduate course on quantum error correction, help organize a national summer school, mentor undergraduates through the Research Experience for Undergraduates program, and engage the public through lectures and outreach. More technically, Professor Dymarsky will pursue two complementary thrusts. The first concerns the approach of TQFT gravity, in which a three-dimensional topological quantum field theory is promoted to a theory of gravity by being summed over all three-dimensional topologies. Holographically, this theory of gravity is dual to a well-defined ensemble of two-dimensional conformal field theories. The project will study models of TQFT gravity based on various non-Abelian Chern-Simons-type theories, with the goal of elucidating the sum over topologies. This research will also shed light on the properties of the boundary ensemble, the role of wormholes, ensemble averaging, and the factorization puzzle in the gravitational path integral. The second thrust will apply the Krylov-space formalism to holographic systems. It will reformulate the algebraic approach to spacetime emergence in terms of Krylov methods, providing a geometric interpretation of Krylov complexity. Building on this connection, the project will also pursue a refined bound on quantum chaos. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.