QED and String Theory
  We analyze the D9-D9bar system in type IIB string theory using Dp-brane probes. It is shown that the world-volume theory of the probe Dp-brane contains two-dimensional and four-dimensional QED in the cases with p=1 and p=3, respectively, and some applications of the realization of these well-studied quantum field theories are discussed. In particular, the two-dimensional QED (the Schwinger model) is known to be a solvable theory and we can apply the powerful field theoretical techniques, such as bosonization, to study the D-brane dynamics. The tachyon field created by the D9-D9bar strings appears as the fermion mass term in the Schwinger model and the tachyon condensation is analyzed by using the bosonized description. In the T-dualized picture, we obtain the potential between a D0-brane and a D8-D8bar pair using the Schwinger model and we observe that it consists of the energy carried by fundamental strings created by the Hanany-Witten effect and the vacuum energy due to a cylinder diagram. The D0-brane is treated quantum mechanically as a particle trapped in the potential, which turns out to be a system of a harmonic oscillator.   As another application, we obtain a matrix theory description of QED using Taylor's T-duality prescription, which is actually applicable to a wide variety of field theories including the realistic QCD. We show that the lattice gauge theory is naturally obtained by regularizing the matrix size to be finite. 
Shigeki Sugimoto, Kazuyoshi Takahashi