Chaotic duality in string theory

We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional $\mathcal{N}=1\mathrm{}$ 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 $P^2$ blown up at a point, we find periodic and quasiperiodic 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.