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

摘要

Here, a scenario is proposed, according to which a generic self-organizedcritical (SOC) system can be looked upon as a Witten-type topological fieldtheory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST)symmetry. One of the conditions for the SOC is the slow driving noise, whichunambiguously suggests Stratonovich interpretation of the correspondingstochastic differential equation (SDE). This, in turn, necessitates the use ofParisi-Sourlas-Wu stochastic quantization procedure, which straightforwardlyleads to a model with BRST-exact action, i.e., to a W-TFT. In the parameterspace of the SDE, there must exist full-dimensional regions where theBRST-symmetry is spontaneously broken by instantons, which in the context ofSOC are essentially avalanches. In these regions, the avalanche-type SOCdynamics is liberated from overwise a rightful dynamics-less W-TFT, and aGoldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent modulii ofinstantons (avalanches) and being gapless are responsible for the criticalavalanche distribution in the low-energy, long-wavelength limit. The abovearguments are robust against moderate variations of the SDE's parameters andthe criticality is "self-tuned". The proposition of this paper suggests thatthe machinery of W-TFTs may find its applications in many different areas ofmodern science studying various physical realizations of SOC. It also suggeststhat there may in principle exist a connection between some of SOC's and theconcept of topological quantum computing.