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Open string modes at brane intersections

Daniel Arean, Alfonso V. Ramallo

TL;DR

This work develops a general framework for open-string fluctuations at BPS brane intersections by treating one brane as a probe in the near-horizon geometry of another. For D3-D5 and D3-D3 defects, the authors obtain analytic fluctuation spectra via exact decoupling and hypergeometric solutions, and they connect these modes to operators in the corresponding defect field theories, including detailed operator dimensions and SU(2)×SU(2) quantum numbers. They also map other intersections to Schrödinger problems, employ WKB methods, and perform numerical computations to obtain spectra, validating degeneracy patterns dictated by underlying supersymmetry. The results illuminate how mass deformations (finite brane separation) generate discrete spectra and reveal Higgs-branch structures in the D3-D3 system, while highlighting limitations due to backreaction and curvature in the holographic setup. Overall, the paper advances defect holography with fundamental matter by providing explicit spectra, fluctuation/operator dictionaries, and methodological tools for a broad class of brane intersections.

Abstract

We study systematically the open string modes of a general class of BPS intersections of branes. We work in the approximation in which one of the branes is considered as a probe embedded in the near-horizon geometry generated by the other type of branes. We mostly concentrate on the D3-D5 and D3-D3 intersections, which are dual to defect theories with a massive hypermultiplet confined to the defect. In these cases we are able to obtain analytical expressions for the fluctuation modes of the probe and to compute the corresponding mass spectra of the dual operators in closed form. Other BPS intersections are also studied and their fluctuation modes and spectra are found numerically.

Open string modes at brane intersections

TL;DR

This work develops a general framework for open-string fluctuations at BPS brane intersections by treating one brane as a probe in the near-horizon geometry of another. For D3-D5 and D3-D3 defects, the authors obtain analytic fluctuation spectra via exact decoupling and hypergeometric solutions, and they connect these modes to operators in the corresponding defect field theories, including detailed operator dimensions and SU(2)×SU(2) quantum numbers. They also map other intersections to Schrödinger problems, employ WKB methods, and perform numerical computations to obtain spectra, validating degeneracy patterns dictated by underlying supersymmetry. The results illuminate how mass deformations (finite brane separation) generate discrete spectra and reveal Higgs-branch structures in the D3-D3 system, while highlighting limitations due to backreaction and curvature in the holographic setup. Overall, the paper advances defect holography with fundamental matter by providing explicit spectra, fluctuation/operator dictionaries, and methodological tools for a broad class of brane intersections.

Abstract

We study systematically the open string modes of a general class of BPS intersections of branes. We work in the approximation in which one of the branes is considered as a probe embedded in the near-horizon geometry generated by the other type of branes. We mostly concentrate on the D3-D5 and D3-D3 intersections, which are dual to defect theories with a massive hypermultiplet confined to the defect. In these cases we are able to obtain analytical expressions for the fluctuation modes of the probe and to compute the corresponding mass spectra of the dual operators in closed form. Other BPS intersections are also studied and their fluctuation modes and spectra are found numerically.

Paper Structure

This paper contains 47 sections, 282 equations, 3 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Fluctuations of intersecting branes
  3. BPS intersections
  4. Dp-brane background
  5. Fundamental string background
  6. M2-brane background
  7. M5-brane background
  8. M5-brane background
  9. Fluctuations
  10. The exactly solvable case
  11. WKB quantization
  12. Numerical computation
  13. Fluctuations of the D3-D5 system
  14. Type I modes
  15. $Z^+$ spectra
  16. ...and 32 more sections

Figures (3)

  • Figure 1: A general orthogonal intersection of a $p_1$- and $p_2$-brane along $d$ spatial directions.
  • Figure 2: The two branes of the intersection are separated a finite distance. In the figure one of the branes is represented as a one-dimensional object. An open string can be stretched between the two branes.
  • Figure 3: The Schrödinger potential $V(y)$ of eq. (\ref{['potential']}).