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Non-abelian Brane Intersections

Neil R. Constable, Robert C. Myers, Oyvind Tafjord

TL;DR

The paper constructs and analyzes a non-abelian D-string configuration where the strings form a fuzzy four-sphere funnel that expands into orthogonal D5-branes, interpreted as D-strings ending on D5-branes. It provides a dual D5-brane description with a homogeneous instanton on S^4, demonstrates matching energy and RR charges in the large $N$ (or large $n$) limit, and reveals a universal small-$R$ funnel behavior transitioning to a harmonic large-$R$ regime. The work generalizes to dyonic strings, studies linearized fluctuations on the funnel, and discusses stability despite the lack of supersymmetry. It also explores extensions to other fuzzy geometries and highlights the regime where the two dual descriptions overlap, illustrating a non-supersymmetric yet consistent brane-intersection duality with potential holographic and M-theory implications.

Abstract

We study new solutions of the low-energy equations of motion for the non-abelian D-string. We find a "fuzzy funnel" solution consisting of a noncommutative four-sphere geometry which expands along the length of the D-string. We show that this funnel solution has an interpretation as D-strings ending on a set of orthogonal D5-branes. Although not supersymmetric, the system appears to be stable within this framework. We also give a dual description of this configuration as a bion spike in the non-abelian world volume theory of coincident D5-branes.

Non-abelian Brane Intersections

TL;DR

The paper constructs and analyzes a non-abelian D-string configuration where the strings form a fuzzy four-sphere funnel that expands into orthogonal D5-branes, interpreted as D-strings ending on D5-branes. It provides a dual D5-brane description with a homogeneous instanton on S^4, demonstrates matching energy and RR charges in the large (or large ) limit, and reveals a universal small- funnel behavior transitioning to a harmonic large- regime. The work generalizes to dyonic strings, studies linearized fluctuations on the funnel, and discusses stability despite the lack of supersymmetry. It also explores extensions to other fuzzy geometries and highlights the regime where the two dual descriptions overlap, illustrating a non-supersymmetric yet consistent brane-intersection duality with potential holographic and M-theory implications.

Abstract

We study new solutions of the low-energy equations of motion for the non-abelian D-string. We find a "fuzzy funnel" solution consisting of a noncommutative four-sphere geometry which expands along the length of the D-string. We show that this funnel solution has an interpretation as D-strings ending on a set of orthogonal D5-branes. Although not supersymmetric, the system appears to be stable within this framework. We also give a dual description of this configuration as a bion spike in the non-abelian world volume theory of coincident D5-branes.

Paper Structure

This paper contains 9 sections, 98 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Review of the D3$\perp$D1-brane system
  3. D-strings growing into D5-branes
  4. D5-branes growing D-strings
  5. Generalization to dyonic strings
  6. Linearized fluctuations
  7. Discussion
  8. The $G^i$ matrices
  9. Homogeneous instantons

Figures (2)

  • Figure 1: The shape of D-string (solid curve) and fundamental string (dashed curve) spikes extending from a set of orthogonal D5-branes. We have set $N=N_fg_s$ so that the profiles overlap for small $\sigma$.
  • Figure 2: (a) Schematic picture of strings ending on a brane. The endpoint of the strings has a charge which is carried away by flux lines on the brane. Alternatively one can think of the flux lines as a continuation of the strings, smeared over the angular directions. (b) In reality the strings pull on the brane, creating a spiked surface.