Ghost-Matter Mixing and Feigenbaum Universality in String Theory

TL;DR

This paper explores how ghost-matter mixing backgrounds in string theory induce stochastic RG flows that exhibit Feigenbaum universality, linking chaos theory to string dynamics and brane-like geometries.

Contribution

It demonstrates the emergence of Feigenbaum constants in string theory RG equations and connects chaos theory with brane-like backgrounds in superstring models.

Findings

RG equations become non-Markovian Fokker-Planck equations

Feigenbaum constant appears in the scaling of space-time curvatures

Fixed points correspond to period doubling in RG flow

Abstract

Brane-like vertex operators, defining backgrounds with the ghost-matter mixing in NSR superstring theory, play an important role in a world-sheet formulation of D-branes and M theory, being creation operators for extended objects in the second quantized formalism. In this paper we show that dilaton's beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations which solutions describe superstrings in curved space-times with brane-like metrics.We show that Feigenbaum universality constant $\delta=4,669...$ describing transitions from order to chaos in a huge variety of dynamical systems, appears analytically in these RG equations. We find that the appearance of this constant is related to the scaling of relative space-time curvatures at fixed points of the RG flow. In this picture the fixed points correspond to the period doubling of Feigenbaum iterational schemes.