Duality cascades and duality walls

TL;DR

This paper analyzes duality cascades in quiver gauge theories using Cartan matrices, revealing conditions for their termination and proposing UV completions via little string theories.

Contribution

It introduces a Cartan matrix framework for duality cascades and identifies conditions leading to duality walls and potential UV completions.

Findings

Duality cascades correspond to Weyl reflections in Cartan matrices.

Cascades with affine ADE Cartan matrices can extend indefinitely.

Non-affine cases can reach a duality wall, suggesting a UV completion.

Abstract

We recast the phenomenon of duality cascades in terms of the Cartan matrix associated to the quiver gauge theories appearing in the cascade. In this language, Seiberg dualities for the different gauge factors correspond to Weyl reflections. We argue that the UV behavior of different duality cascades depends markedly on whether the Cartan matrix is affine ADE or not. In particular, we find examples of duality cascades that can't be continued after a finite energy scale, reaching a "duality wall", in terminology due to M. Strassler. For these duality cascades, we suggest the existence of a UV completion in terms of a little string theory.