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

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.

12 pages, 1 figure; v2 is the published version, extensively revised as compared to v1

References in corpus (20)

• Fault-tolerant quantum computation by anyons
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Collective Transport: From Superconductors to Earthquakes
• Emergent Traffic Jams
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• The Field Theory Approach to Percolation Processes
• Self-organization without conservation: true or just apparent scale-invariance?
• Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators
• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Avalanches in mean-field models and the Barkhausen noise in spin-glasses
• Stochastic Gravity
• Relating Field Theories via Stochastic Quantization
• On Synchronization in a Lattice Model of Pulse-Coupled Oscillators
• Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Supersymmetry approach to the random heteropolymer theory

Cited by in corpus (8)

• Introduction to Supersymmetric Theory of Stochastics
• Criticality or Supersymmetry Breaking ?
• Ubiquitous order known as chaos
• Topological field theory of dynamical systems
• Generalized Grassmann algebras and applications to stochastic processes
• Supersymmetric Theory of Stochastic ABC Model: A Numerical Study
• Transfer operators and topological field theory
• Witten-type topological field theory of self-organized criticality for stochastic neural networks