Chaotic Duality in String Theory

TL;DR

This paper explores the complex and chaotic behavior of renormalization group flows in certain supersymmetric gauge theories with gravity duals, revealing fractal structures and exotic phenomena like duality walls.

Contribution

It provides the first detailed analysis of chaos and exotic features in RG flows of N=1 supersymmetric gauge theories with gravity duals, including supergravity constructions.

Findings

RG flows are often chaotic with duality walls.

Duality wall height exhibits self-similar fractal structure.

Gauge couplings show periodic and quasi-periodic behavior.

Abstract

We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional N=1 supersymmetric gauge theories with gravity duals. The gauge theories we study arise as the world-volume theory on a set of D-branes at a Calabi-Yau singularity where a del Pezzo surface shrinks to zero size. Based mainly on field theory analysis, we find evidence that such flows are often chaotic and contain exotic features such as duality walls. For a gauge theory where the del Pezzo is the Hirzebruch zero surface, the dependence of the duality wall height on the couplings at some point in the cascade has a self-similar fractal structure. For a gauge theory dual to CP^2 blown up at a point, we find periodic and quasi-periodic behavior for the gauge theory couplings that does not violate the a-conjecture. Finally, we construct supergravity duals for these del Pezzos that match our field theory beta functions.