Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry

TL;DR

This paper proposes that self-organized criticality (SOC) systems can be modeled as Witten-type topological field theories with spontaneously broken BRST symmetry, linking critical avalanche dynamics to topological field theory concepts.

Contribution

It introduces a novel theoretical framework connecting SOC to topological field theories and BRST symmetry breaking, providing a new perspective on critical phenomena.

Findings

SOC corresponds to a Witten-type topological field theory with broken BRST symmetry.

Avalanches in SOC are modeled as instantons causing spontaneous symmetry breaking.

Critical avalanche distributions are explained by gapless Goldstino modes in the theory.

Abstract

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST-symmetry is spontaneously broken by instantons, which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent modulii of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is "self-tuned". The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some of SOC's and the concept of topological quantum computing.