Self-similar inverse cascade from generalized symmetries

TL;DR

This paper reveals how higher-form symmetries can induce self-similar inverse cascades in turbulent systems, providing a new fundamental organizing principle for non-equilibrium phenomena and the emergence of large-scale structures.

Contribution

It introduces a novel mechanism where higher-form symmetries drive inverse cascades, demonstrated through axion electrodynamics with analytical scaling exponents.

Findings

Higher-form symmetries induce inverse cascades in turbulence.

Conserved charges from 1-form symmetries lead to large-scale structures.

Universal scaling behavior characterized by analytical exponents.

Abstract

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.