A new way to handle twisted quantum field theories

J̄J-deformations twist conformal field theories in ways that break standard calculation methods. This work reformulates the problem using Riemann bilinear identities—a classical tool—to convert the deformation into a dressing that works systematically at all orders. The authors calculate how partition functions and operator weights change under deformation while preserving deep symmetries, then verify the method on concrete examples including string theory backgrounds.