Fusion category symmetry often implies equal particle and soliton masses.

Clay Córdova, Diego García-Sepúlveda, and Nicholas Holfester of the University of Chicago have demonstrated a surprising connection between particles and solitons in two-dimensional quantum chromodynamics. Their work reveals that a specific type of symmetry, described mathematically by a fusion category, can force particles and solitons to share the same mass, a result challenging the conventional understanding of these distinct quantum excitations. This symmetry breaks down at long distances, creating multiple possible vacua, and the researchers map the resulting complex relationships using “quiver diagrams” where nodes represent vacua and arrows depict excited states. The findings offer new insight into strongly coupled physics and the infrared spectrum of gauge theories. A specific symmetry within two-dimensional quantum chromodynamics dictates that certain particles and solitons must possess identical masses, a result challenging conventional expectations about these distinct quantum entities. This unexpected equivalence arises from a “finite non-invertible symmetry” described by a mathematical structure known as a fusion category, which governs the interactions within the theory. The research, focused on gapped theories, uses an interval compactification from a three-dimensional topological quantum field theory to identify the fusion category responsible for this symmetry. This approach allows for the…