QED and String Theory

We analyze the D9-D9bar system in type IIB string theory using Dp-braneprobes. It is shown that the world-volume theory of the probe Dp-brane containstwo-dimensional and four-dimensional QED in the cases with p=1 and p=3,respectively, and some applications of the realization of these well-studiedquantum field theories are discussed. In particular, the two-dimensional QED(the Schwinger model) is known to be a solvable theory and we can apply thepowerful field theoretical techniques, such as bosonization, to study theD-brane dynamics. The tachyon field created by the D9-D9bar strings appears asthe fermion mass term in the Schwinger model and the tachyon condensation isanalyzed by using the bosonized description. In the T-dualized picture, weobtain the potential between a D0-brane and a D8-D8bar pair using the Schwingermodel and we observe that it consists of the energy carried by fundamentalstrings created by the Hanany-Witten effect and the vacuum energy due to acylinder diagram. The D0-brane is treated quantum mechanically as a particletrapped in the potential, which turns out to be a system of a harmonicoscillator. As another application, we obtain a matrix theory description of QED usingTaylor's T-duality prescription, which is actually applicable to a wide varietyof field theories including the realistic QCD. We show that the lattice gaugetheory is naturally obtained by regularizing the matrix size to be finite.Comment: 33 pages, Latex, 4 figures, a reference adde