Self-similar inverse cascade from generalized symmetries

We investigate the role of generalized symmetries in driving non-equilibrium and non-linear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved quantities integrated over the entire space, such as helicity in three spatial dimensions, the influence of higher-form symmetries, whose conserved charges are defined by integration over subspaces, remains largely unexplored. We demonstrate a novel mechanism where higher-form symmetries naturally induce a self-similar inverse cascade. Taking axion electrodynamics with non-linear topological interaction as a paradigmatic example, we show that the conserved charge associated with its 1-form symmetry drives the system toward large-scale coherent structures through a universal scaling behavior characterized by analytically determined scaling exponents. Our findings suggest that higher-form symmetries can provide a fundamental organizing principle for understanding non-equilibrium phenomena and the emergence of coherent structures in turbulent systems.

💡 Research Summary

The paper investigates how generalized, higher‑form symmetries can drive inverse‑cascade dynamics in non‑equilibrium, nonlinear systems, using axion electrodynamics with a nonlinear topological coupling as a concrete example. Conventional turbulence theory attributes inverse cascades to conserved quantities that are integrated over the whole spatial domain (e.g., helicity in three dimensions). In contrast, higher‑form symmetries possess conserved charges defined on sub‑manifolds (lines, surfaces), and the authors ask whether such charges can generate a cascade without invoking a global invariant.

They consider a (3+1)‑dimensional theory of a massless axion ϕ coupled to a U(1) gauge field aμ with Lagrangian
S = ∫ d⁴x