QED and String Theory

Abstract

We analyze the D9-D9 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-D9 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-D8 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. * See [1] for a review.The D9-D9 system is an unstable D-brane system and it is known that there is a tachyon field created by the open string stretched between the D9-brane and the D9brane. When the tachyon field homogeneously condenses, the D9-D9 pairs are believed to be annihilated.[5, 6, 1] More interestingly, when the tachyon field takes a vortex configuration, it represents a D7-brane.[7, 1] The lower dimensional D-branes can be similarly constructed by non-trivial tachyon configurations in the D9-D9 system.[8]When we put the D-brane probe in this system, the tachyon field is interpreted as the fermion mass parameter in the world-volume theory. We will observe these phenomena in terms of the bosonized description of the Schwinger model.When we compactify the direction parallel to the D-brane probe to a torus, we can T-dualize the system to obtain a lower dimensional description of QED. The T-duality prescription given in [9,10,11,12] can also be applied to the world-volume theory on the D-brane in the presence of the D9-D9 pairs. Actually, since the essential step in the prescription is just the Fourier transformation, it is applicable to any field theory compactified on a torus. By T-dualizing all the space-time directions, we obtain a matrix theory description. The size of the matrix variables here is infinite, since there are infinitely many copies of the D-branes in the covering space. We shall show that when we regularize the matrix size to be finite in this matrix theory description, we naturally obtain usual lattice gauge theory.The paper is organized as follows. First we summa...

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