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Quantum field theory is hard for several reasons, for example one can rarely compute perturbation series (=Feynman integrals) at large loop order, and even if you can, the series diverges. Conversely, intrinsically non-perturbative approaches like the functional renormalization group require approximations that are often not easy to control, or have unclear relations to perturbative computations.
Tropical field theory is a new approach for solving these issues for a generic theory without restricting to unphysical boundary cases. It keeps almost all qualitative and combinatorial features of perturbative QFT (in particular all non-planar diagrams, renormalization, relative numerical importance of Feynman integrals, and divergence of perturbation series), while at the same time reducing the analytic complexity, and establishing a rigorous connection to non-perturbative functional/path integral methods of QFT. Based on 2512.21091 with Erik.