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TASI Lectures on D-Branes

Joseph Polchinski

TL;DR

The work surveys how D-branes emerge as fundamental nonperturbative objects in string theory through a sequence of topics: open and unoriented strings, T-duality and the birth of D-branes, supersymmetric extensions with RR charges, and advanced D-brane mechanics including bound states. It builds a cohesive framework linking Born-Infeld dynamics, RR couplings, and brane worldvolume theories to dualities (T- and U-duality) and to M-theory, illustrating how D-branes realize seemingly disparate phenomena such as instantons, probes of geometry, and microscopic black holes. The lectures demonstrate both technical derivations (brane tensions, actions, and charge couplings) and broad physical consequences (eleventh dimension, bound-state spectra, and entropy counting), arguing that D-branes are central to a nonperturbative, unified description of string theory. Together, they illuminate how branes encode nonperturbative dynamics, geometry, and holographic connections that underpin the deeper structure of the theory.

Abstract

This is an introduction to the properties of D-branes, topological defects in string theory on which string endpoints can live. D-branes provide a simple description of various nonperturbative objects required by string duality, and give new insight into the quantum mechanics of black holes and the nature of spacetime at the shortest distances. The first two thirds of these lectures closely follow the earlier ITP lectures hep-th/9602052, written with S. Chaudhuri and C. Johnson. The final third includes more extensive applications to string duality.

TASI Lectures on D-Branes

TL;DR

The work surveys how D-branes emerge as fundamental nonperturbative objects in string theory through a sequence of topics: open and unoriented strings, T-duality and the birth of D-branes, supersymmetric extensions with RR charges, and advanced D-brane mechanics including bound states. It builds a cohesive framework linking Born-Infeld dynamics, RR couplings, and brane worldvolume theories to dualities (T- and U-duality) and to M-theory, illustrating how D-branes realize seemingly disparate phenomena such as instantons, probes of geometry, and microscopic black holes. The lectures demonstrate both technical derivations (brane tensions, actions, and charge couplings) and broad physical consequences (eleventh dimension, bound-state spectra, and entropy counting), arguing that D-branes are central to a nonperturbative, unified description of string theory. Together, they illuminate how branes encode nonperturbative dynamics, geometry, and holographic connections that underpin the deeper structure of the theory.

Abstract

This is an introduction to the properties of D-branes, topological defects in string theory on which string endpoints can live. D-branes provide a simple description of various nonperturbative objects required by string duality, and give new insight into the quantum mechanics of black holes and the nature of spacetime at the shortest distances. The first two thirds of these lectures closely follow the earlier ITP lectures hep-th/9602052, written with S. Chaudhuri and C. Johnson. The final third includes more extensive applications to string duality.

Paper Structure

This paper contains 32 sections, 134 equations, 13 figures.

Table of Contents

  1. Lecture 1: Open and Unoriented Bosonic Strings
  2. Open Strings
  3. Chan-Paton Factors
  4. Unoriented Strings
  5. Lecture 2: $T$-Duality
  6. Self-Duality of Closed Strings
  7. $T$-Duality of Open Strings
  8. $T$-Duality with Chan-Paton Factors and Wilson Lines
  9. D-Brane Dynamics
  10. The D-Brane Action
  11. D-Brane Tension
  12. Unoriented Strings and Orientifolds.
  13. Lecture 3: Superstrings and $T$-Duality
  14. Open Superstrings
  15. Closed Superstrings
  16. ...and 17 more sections

Figures (13)

  • Figure 1: a) Scattering of open strings. b) Conformally transformed world-sheet.
  • Figure 2: Open string with Chan-Paton degrees of freedom.
  • Figure 3: a) Torus formed by identifying opposite edges. b) Klein bottle formed by identification with a twist.
  • Figure 4: Projective plane formed by identifying opposite points on the disk as shown. This can also be regarded as a sphere with a crosscap inserted.
  • Figure 5: Open strings with endpoints attached to a hyperplane. The dashed planes are periodically identified. The strings shown have winding numbers zero and one.
  • ...and 8 more figures