QED and String Theory

TL;DR

This paper explores the realization of quantum electrodynamics (QED) within string theory frameworks, analyzing D-brane systems and their associated field theories, and applies these insights to matrix models and potential connections to QCD.

Contribution

It demonstrates how D-brane probe world-volume theories can realize 2D and 4D QED, and develops matrix theory descriptions of QED with applications to lattice gauge theories.

Findings

Two-dimensional QED (Schwinger model) is solvable and applicable to D-brane dynamics.

Tachyon condensation is studied via bosonization in the D-brane system.

Matrix theory provides a natural regularization of lattice gauge theories.

Abstract

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.