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(Half) a Lecture on D-branes

C. Bachas

TL;DR

The work argues that D-branes are fundamental non-perturbative RR-charged objects essential to string dualities and gravity. By combining open- and closed-string perspectives, Polchinski derives the D-brane tension and RR charge, shows their BPS nature leads to no net force between parallel branes, and establishes their charges via a Dirac-like quantization. The discussion connects D-brane world-volume dynamics to gauge theories through dimensional reduction, and highlights T-duality and Lorentz invariance as guiding principles that generate the Born-Infeld action and Wess-Zumino terms. Collectively, these results underpin a broad program linking spacetime geometry, gauge theory, and dualities, with profound implications for black holes, M-theory, and matrix model formulations.

Abstract

This is a concise foreword to, rather than a review of D-brane physics.

(Half) a Lecture on D-branes

TL;DR

The work argues that D-branes are fundamental non-perturbative RR-charged objects essential to string dualities and gravity. By combining open- and closed-string perspectives, Polchinski derives the D-brane tension and RR charge, shows their BPS nature leads to no net force between parallel branes, and establishes their charges via a Dirac-like quantization. The discussion connects D-brane world-volume dynamics to gauge theories through dimensional reduction, and highlights T-duality and Lorentz invariance as guiding principles that generate the Born-Infeld action and Wess-Zumino terms. Collectively, these results underpin a broad program linking spacetime geometry, gauge theory, and dualities, with profound implications for black holes, M-theory, and matrix model formulations.

Abstract

This is a concise foreword to, rather than a review of D-brane physics.

Paper Structure

This paper contains 14 sections, 63 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Ramond-Ramond fields
  3. Chiral Bispinors
  4. Free Field Equations
  5. No RR Charges in Perturbation Theory
  6. D(irichlet) branes
  7. Definition
  8. Static Force: Field-Theory Calculation
  9. Static Force: String Calculation
  10. Charge Quantization
  11. Gauge Theory and Geometry
  12. Non-commutative Space-time
  13. T-duality
  14. The Power of Lorentz Invariance

Figures (3)

  • Figure 1: Two D-branes interacting through the exchange of a closed string. The diagram has a dual interpretation as Casimir force due to vacuum fluctuations of open strings.
  • Figure 2: A 1-brane creates a 3-index "electric" field $F_{(3)}$. Electric flux in d=4 space-time dimensions is given by an integral of the dual vector over a 1-sphere. The magnetic potential is a scalar field with a discontinuity across the depicted Dirac sheet singularity.
  • Figure 3: A D-brane sandwitch, and the four types of open strings giving rise to massless states in the coincidence limit.