Lectures on D-branes

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.

Figures (8)

• Figure 1: The web of dualities relating the ten-dimensional superstring theories and ${\cal M}$ theory, as described in the text.
• Figure 2: 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 3: A 1-brane creates a 3-index "electric" field $H^{(3)}$. Electric flux in d=4 space-time dimensions is given by an integral of the dual vector over a circle $S_{(1)}$. The 'magnetic' potential is a scalar field, coupling to point-like (Euclidean) instantons, and jumping discontinuously across the depicted sheet singularity.
• Figure 4: The semi-circles are two snapshots of an open string at fixed radial time $\xi^0 = {\rm log}|z|$. A charge is conserved when its time variation can be expressed as a holomorphic plus antiholomorphic contour integral around the shaded region in the upper complex plane. This means that the contributions of the linear segments on the worldsheet boundary should vanish.
• Figure 5: Two D-particles scattering with relative velocity $v$ and impact parameter $b$. The broken lines depict a virtual pair of oriented strings being stretched by the relative motion. The imaginary part of the phase shift gives the probability that these virtual strings materialize.