Duality Walls, Duality Trees and Fractional Branes

TL;DR

This paper analyzes the RG flow of N=1 quiver gauge theories from D-branes on singularities, revealing duality walls where the theory's degrees of freedom diverge, and explores related dualities and symmetries.

Contribution

It computes NSVZ beta functions for a broad class of quiver theories, identifying duality walls and T-duality-like symmetries in the holographic dual.

Findings

Identification of duality walls at finite energy scales.

Non-zero beta functions in the presence of fractional branes.

Connection between quiver symmetries and T-duality.

Abstract

We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at which the number of degrees of freedom becomes infinite, and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory.