[Paper Review] Lectures on D-branes

Constantin P. Bachas|ArXiv.org|Jun 24, 1998

Black Holes and Theoretical PhysicsPhysics and Astronomy212 references178 citations

TL;DR

This paper provides a foundational introduction to D-branes in string theory, emphasizing their role as dynamical objects that generalize quarks in QCD and are required for consistency in string theory. It presents key results such as Polchinski's original calculation of D-brane tension, the interpretation of D-brane scattering via T-duality, and the use of D-branes to probe quantum gravity and black hole entropy, establishing their central role in the 'second string revolution' and dualities among string theories.

ABSTRACT

This is an introduction to the physics of D-branes. Topics covered include Polchinski's original calculation, a critical assessment of some duality checks, D-brane scattering, and effective worldvolume actions.

Motivation & Objective

• To provide a pedagogical introduction to D-branes for researchers with background in perturbative string theory.
• To clarify the physical and mathematical structure of D-branes, including their tension, charges, and dynamics via worldvolume actions.
• To establish the role of D-branes in realizing dualities and in the 'second string revolution' that unified string theories.
• To connect D-brane physics to key problems in quantum gravity, such as black hole entropy and the microscopic origin of thermodynamics.
• To serve as a springboard for advanced topics like brane engineering, Seiberg duality, and the M-theory unification.

Proposed method

• Uses Polchinski's original calculation of D-brane tension via open string scattering amplitudes to derive the D-brane tension as $ T_p = \frac{1}{(2\pi)^p \alpha'^{(p+1)/2}} $.
• Applies T-duality and S-duality transformations to relate different brane configurations, such as the creation of a D3-brane from a fundamental string and NS5-brane crossing.
• Analyzes D-brane scattering and anomalous charge inflow using the Weyl equation in T-dualized frames, showing fermionic zero modes on intersections.
• Derives effective worldvolume actions for D-branes using boundary conformal field theory and supersymmetry constraints.
• Applies the Atiyah-Singer index theorem and $\hat{A}$-genus to compute anomalies in D-brane systems, ensuring consistency via anomaly cancellation.
• Uses brane engineering to model supersymmetric gauge theories and explore Seiberg duality through intersecting brane configurations.

Experimental results

Research questions

• RQ1 How do D-branes arise as consistent boundary conditions for open strings, and what determines their tension and charges?
• RQ2 What is the role of D-branes in realizing dualities between different string theories, particularly in the context of the 'second string revolution'?
• RQ3 How can D-branes be used to compute the microscopic degeneracy of BPS black hole states, and what does this reveal about black hole entropy?
• RQ4 What is the physical interpretation of anomalous fermion production when two orthogonal D-branes cross, and how does T-duality explain this?
• RQ5 How do D-branes provide a framework for studying supersymmetric gauge theories and their dualities, such as Seiberg duality?

Key findings

• D-branes are fundamental, intrinsic excitations of string theory whose tension and charges are unambiguously determined by the Regge slope $ \alpha' $ and moduli, making them more than just solitons.
• Polchinski's original calculation confirms that the D-brane tension is $ T_p = \frac{1}{(2\pi)^p \alpha'^{(p+1)/2}} $, consistent with T-duality and S-duality.
• The anomalous creation of a stretched string when two orthogonal D4-branes cross is a topological effect, explained via the T-dual Weyl equation and charge inflow.
• T-duality maps the creation of a fundamental string between two D4-branes to the creation of a D3-brane from a D5-brane and NS5-brane crossing, confirming consistency across dualities.
• The anomaly inflow mechanism ensures that chiral fermions on D-brane intersections are canceled by normal bundle anomalies, preserving gauge and Lorentz invariance.
• D-branes provide a microscopic realization of black hole entropy, with the BPS degeneracy mapped to the moduli space of supersymmetric gauge theories, offering a solution to black hole thermodynamics.