S-duality and Chaos

TL;DR

This paper explores the surprising link between chaos and duality in quantum field theories, proposing that chaotic RG flows can lead to the emergence of dual theories and suggesting a connection to the Riemann-Zeta function.

Contribution

It introduces the novel idea that chaotic renormalization group flows can produce dual quantum field theories and connects this to properties of the Riemann-Zeta function.

Findings

Chaotic RG trajectories can lead to dual field theories.

Strong-weak duality arises from chaotic RG flow.

Conjecture of dual theories related to the Riemann-Zeta function.

Abstract

The Renormalization group in field theories happens to resemble dynamical systems in many ways. In this paper, we discuss the unexpected connection between chaos and duality in field theories. In a sense, that various dual field theories can emerge at the end of chaotic RG trajectories, and hence strong-weak duality in quantum field theory is a direct result of the chaotic flow of the renormalization group. This suggests that various properties of field and string theories could come into existence due to chaotic RG flow. We also conjecture the existence of dual quantum field theories in the half strip of Riemann-Zeta function.