A Trio of Dualities: Walls, Trees and Cascades

TL;DR

This paper investigates the renormalization group flows of certain D3-brane gauge theories on Calabi-Yau singularities, revealing duality cascades, walls, and a classification via Markov-type equations.

Contribution

It introduces the concept of duality walls in gauge theory cascades and connects RG flow classifications to Markov equations for various geometries.

Findings

Identification of duality walls as finite UV limits.

Characterization of dual phases using Markov-type Diophantine equations.

Relation of RG flow classifications to geometric families.

Abstract

We study the RG flow of N=1 world-volume gauge theories of D3-brane probes on certain singular Calabi-Yau threefolds. Taking the gauge theories out of conformality by introducing fractional branes, we compute the NSVZ beta-function and follow the subsequent RG flow in the cascading manner of Klebanov-Strassler. We study the duality trees that blossom from various Seiberg dualities and encode possible cascades. We observe the appearance of duality walls, a finite limit energy scale in the UV beyond which the dualization cascade cannot proceed. Diophantine equations of the Markov type characterize the dual phases of these theories. We discuss how the classification of Markov equations for different geometries into families relates the RG flows of the corresponding gauge theories.