Self-duality, integrability, topological entanglement and a field theory model of two linked rings

Abstract This paper examines the link between the statistical mechanics of polymer systems and field theory, focusing on topologically linked polymer rings in a 4-plat configuration. We derive the partition function and interpret it through the lens of physics of anyons. Using techniques from theory of anyons, we establish the self-duality equations and find solutions that minimize the system’s energy. Under specific conditions, these self-duality equations simplify to the Euclidean sinh-Gordon, cosh-Gordon, or Liouville equations, for which we compute translationally invariant solutions and corresponding polymer densities. Our findings provide new insights into the field-theoretic approach to topologically constrained polymers.