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Fluctuation Spectra of Tilted and Intersecting D-branes from the Born-Infeld Action

Akikazu Hashimoto, Washington Taylor

TL;DR

This work analyzes how fluctuation spectra around tilted and intersecting D-branes on tori match dual gauge-theory descriptions with constant background fields. It demonstrates that the full Born-Infeld action, not just Yang-Mills, is needed to reproduce the exact open-string spectra in nonzero background fields, with a characteristic rescaling of spatial intervals. For branes at angles, a non-abelian Born-Infeld framework (Tseytlin’s symmetrized trace) captures much of the correct structure, but finite-angle discrepancies persist, indicating the need for a more complete non-abelian BI formulation. The study also reveals tachyonic instabilities in non-supersymmetric configurations and frames these instabilities naturally within the gauge-theory language. Overall, the paper highlights deep connections between D-brane physics, Born-Infeld dynamics, and gauge theory, guiding future work on non-abelian BI actions and brane interactions.

Abstract

We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string fluctuation spectrum is reproduced exactly by the gauge theory in the case of vanishing field strength; however, this correspondence breaks down for fixed nonzero field strength. We show that in many cases the full Born-Infeld action correctly captures the low-energy spectrum in the case of non-vanishing field strength. This gives a field theory description of the low-energy physics of systems of diagonally wound branes and branes at angles as considered by Berkooz, Douglas and Leigh. This description extends naturally to non-supersymmetric configurations, where the tachyonic instability associated with brane-anti-brane systems appears as an instability around a saddle point solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the field theory description requires a non-abelian generalization of the Born-Infeld action. We follow Tseytlin's recent proposal for formulating such an action. In the case of intersecting branes, the non-abelian Born-Infeld theory produces a transcendental relation which comes tantalizingly close to reproducing the correct spectrum; however, a discrepancy remains which indicates that a further clarification of the non-abelian Born-Infeld action may be necessary.

Fluctuation Spectra of Tilted and Intersecting D-branes from the Born-Infeld Action

TL;DR

This work analyzes how fluctuation spectra around tilted and intersecting D-branes on tori match dual gauge-theory descriptions with constant background fields. It demonstrates that the full Born-Infeld action, not just Yang-Mills, is needed to reproduce the exact open-string spectra in nonzero background fields, with a characteristic rescaling of spatial intervals. For branes at angles, a non-abelian Born-Infeld framework (Tseytlin’s symmetrized trace) captures much of the correct structure, but finite-angle discrepancies persist, indicating the need for a more complete non-abelian BI formulation. The study also reveals tachyonic instabilities in non-supersymmetric configurations and frames these instabilities naturally within the gauge-theory language. Overall, the paper highlights deep connections between D-brane physics, Born-Infeld dynamics, and gauge theory, guiding future work on non-abelian BI actions and brane interactions.

Abstract

We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string fluctuation spectrum is reproduced exactly by the gauge theory in the case of vanishing field strength; however, this correspondence breaks down for fixed nonzero field strength. We show that in many cases the full Born-Infeld action correctly captures the low-energy spectrum in the case of non-vanishing field strength. This gives a field theory description of the low-energy physics of systems of diagonally wound branes and branes at angles as considered by Berkooz, Douglas and Leigh. This description extends naturally to non-supersymmetric configurations, where the tachyonic instability associated with brane-anti-brane systems appears as an instability around a saddle point solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the field theory description requires a non-abelian generalization of the Born-Infeld action. We follow Tseytlin's recent proposal for formulating such an action. In the case of intersecting branes, the non-abelian Born-Infeld theory produces a transcendental relation which comes tantalizingly close to reproducing the correct spectrum; however, a discrepancy remains which indicates that a further clarification of the non-abelian Born-Infeld action may be necessary.

Paper Structure

This paper contains 11 sections, 93 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Tilted D-branes and the Born-Infeld Action
  3. Review of D-branes and T-duality
  4. 1-brane on $T^2$ with winding $(1, q)$
  5. 1-brane on $T^2$ with winding $(p, q)$
  6. Intersecting Branes and Non-Abelian Born-Infeld
  7. Branes at angles
  8. Yang-Mills fluctuation spectra
  9. Resolving the discrepancy using non-abelian Born-Infeld
  10. Brane-anti-brane configurations
  11. Conclusions

Figures (7)

  • Figure 1: A 2-brane with unit flux quantum and its T-dual
  • Figure 2: A 2-brane with $q$ flux quanta and its T-dual
  • Figure 3: Winding modes of open strings attached to a tilted D-brane are not local from the world-volume observer's point of view.
  • Figure 4: $p$ 2-branes with $q$ flux quanta and the T-dual $(p, q)$ 1-brane
  • Figure 5: (12)-plane cross section of two 4-branes with a constant field strength 2-instanton background and the T-dual intersecting 2-branes.
  • ...and 2 more figures