[Paper Review] Notes on D-Branes

Joseph Polchinski, Clifford V. Johnson+1 more|arXiv (Cornell University)|Feb 10, 1996

Black Holes and Theoretical PhysicsPhysics and Astronomy10 references208 citations

TL;DR

This paper provides a series of lectures on D-branes and orientifolds in the context of heterotic string theory, focusing on their emergence under T-duality. It demonstrates how T-duality relates D-branes and orientifolds, and applies these insights to string duality, offering a foundational understanding of non-perturbative structures in string theory.

ABSTRACT

This is a series of remedial lectures on open and unoriented strings for the heterotic string generation. The particular focus is on the interesting features that arise under T-duality---D-branes and orientifolds. The final lecture discusses the application to string duality. There will be no puns. Lectures presented by J. P. at the ITP from Nov. 16 to Dec. 5, 1995.

Motivation & Objective

• To explain the role of D-branes and orientifolds in open and unoriented string theories.
• To clarify how T-duality relates D-branes to other brane configurations and orientifolds.
• To explore the implications of these structures for string duality.
• To provide a pedagogical foundation for advanced topics in string theory using T-duality as a unifying framework.

Proposed method

• Uses T-duality as a central tool to relate different brane configurations and orientifold planes.
• Applies the formalism of open strings with boundary conditions to derive D-brane states.
• Introduces orientifolds via projection operators that implement worldsheet orientation reversal.
• Analyzes the spectrum of open strings ending on D-branes and orientifold planes.
• Demonstrates consistency conditions for D-branes and orientifolds under T-duality.
• Applies the derived structures to explore dualities between different string theories.

Experimental results

Research questions

• RQ1 How do D-branes arise naturally under T-duality in heterotic string theory?
• RQ2 What are the conditions for the existence of D-branes and orientifolds in unoriented string theories?
• RQ3 How does T-duality relate D-branes to other brane types and orientifold planes?
• RQ4 What role do D-branes and orientifolds play in the duality web of string theory?
• RQ5 How can the spectrum of open strings ending on D-branes and orientifolds be consistently quantized?

Key findings

• D-branes emerge as T-dual images of other brane configurations, providing a unified description of various D-brane types.
• Orientifolds are consistently defined via worldsheet projection, preserving spacetime supersymmetry in specific cases.
• T-duality maps D-branes to other D-branes and orientifolds to orientifolds, preserving the consistency of the spectrum.
• The presence of D-branes and orientifolds allows for a consistent description of open strings in unoriented theories.
• The framework enables the construction of dual descriptions of string theories, supporting the web of string dualities.
• The analysis reveals that D-branes and orientifolds are essential for realizing non-perturbative symmetries in heterotic string theory.