Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Duality Walls in String Theory

Amihay Hanany, Johannes Walcher

TL;DR

The paper presents a tractable toy model for duality walls in string theory by studying Seiberg duality cascades on branes at the ${{{ m C}_3}/{ m Z}_3}$ orbifold. It combines naive beta-function dynamics with a $(p,q)$-charge/monodromy framework to obtain closed-form cascade solutions and track the emergence of a wall at finite energy, where two couplings flow to the UV while the wall is approached exponentially. The key results show that the wall position is piecewise linear in the initial conditions, while the approach to the wall is governed by a universal exponent (unity) in this setup; special initial conditions yield explicit breakpoints and a sequence $1,4,12,33,rac{}{}$ for the wall location in the $d=3$ case. Although the setup is unphysical due to naive beta-functions, the analysis illuminates how duality cascades can organize themselves, form walls, and potentially relate to holographic entropy and moduli-space singularities 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.

On Duality Walls in String Theory

TL;DR

The paper presents a tractable toy model for duality walls in string theory by studying Seiberg duality cascades on branes at the orbifold. It combines naive beta-function dynamics with a -charge/monodromy framework to obtain closed-form cascade solutions and track the emergence of a wall at finite energy, where two couplings flow to the UV while the wall is approached exponentially. The key results show that the wall position is piecewise linear in the initial conditions, while the approach to the wall is governed by a universal exponent (unity) in this setup; special initial conditions yield explicit breakpoints and a sequence for the wall location in the case. Although the setup is unphysical due to naive beta-functions, the analysis illuminates how duality cascades can organize themselves, form walls, and potentially relate to holographic entropy and moduli-space singularities 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.

Paper Structure

This paper contains 13 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The underlying quiver
  3. D-brane interpretation
  4. Comments on RG flow
  5. Duality cascades
  6. Seiberg duality transformations
  7. Coupling constants and energy scale
  8. The cascade
  9. One branch of the tree
  10. The cascade in terms of $(p,q)$ charges
  11. Explicit solution
  12. The Wall
  13. The position of the wall

Figures (2)

  • Figure 1: The quiver
  • Figure :