Chaotic Duality in String Theory

TL;DR

This work probes renormalization group dynamics of four-dimensional ${\cal N}=1$ gauge theories with gravity duals arising from D-branes at Calabi–Yau del Pezzo singularities. By employing exceptional collections and a simplicial view of the coupling space, it uncovers chaotic cascades, duality walls, and fractal wall structures (notably for ${\mathbb F}_0$) alongside quasiperiodic behavior in ${\rm dP}_1$ flows, and it constructs KT-like supergravity solutions that reproduce key beta-function data. The results demonstrate rich, geometry-driven RG behavior beyond KS-type flows, bridging field theory cascades with their gravity duals and revealing intricate structures such as self-similarity and Poincaré-like dynamics in coupling space. These findings deepen our understanding of AdS/CFT beyond conformal points and highlight new pathways to model realistic gauge-theory phenomena via string-theoretic constructions.

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.