On Duality Walls in String Theory

TL;DR

This paper investigates the phenomenon of duality walls in string theory by analyzing Seiberg dualities in quiver gauge theories at orbifold singularities, revealing the scale and behavior of these walls through a specific example.

Contribution

It provides a detailed study of duality walls in string theory using Seiberg dualities on branes at orbifold singularities, including the determination of wall position and critical exponents.

Findings

The wall position is piecewise linear.

The critical exponent governing approach to the wall appears constant.

The study offers insights into the behavior of duality cascades in string theory.

Abstract

Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated quiver has Lorentzian signature. We here study sequences of Seiberg dualities on branes at the C_3/Z_3 orbifold singularity. We use the naive beta functions to define an (unphysical) scale along the cascade. We determine, as a function of initial conditions, the scale of the wall as well as the critical exponent governing the approach to it. The position of the wall is piecewise linear, while the exponent appears to be constant. We comment on the possible implications of these results for physical walls.