Renormalizability of the open string sigma model and emergence of D-branes

TL;DR

This paper rederives one-loop divergences in the open string sigma model, introduces a new boundary coupling, and explains how D-branes naturally emerge when boundary conditions change due to background fields.

Contribution

It identifies a new boundary coupling in the open string sigma model and demonstrates its role in the emergence of D-branes through boundary condition transitions.

Findings

Introduction of a new boundary one-form field coupled to the normal derivative.

Calculation of the beta function for the extended model.

Mechanism for D-brane emergence via boundary condition change.

Abstract

Rederiving the one-loop divergences for the most general coupling of the open string sigma model by the heat kernel technique, we distinguish the classical background field from the mean field of the effective action. The latter is arbitrary, i.e. does not fulfil the boundary conditions. As a consequence a new divergent counter term strongly suggests the introduction of another external one-form field (beside the usual gauge field), coupled to the normal derivative at the boundary. Actually such a field has been proposed in the literature for different reasons, but its full impact never seems to have thoroughly investigated before. The beta function for the resulting renormalizable model is calculated and the consequences are discussed, including the ones for the Born-Infeld action. The most exciting property of the new coupling is that it enters the coefficient in front of the normal derivative in Neumann boundary conditions. For certain values of the background fields this coefficient vanishes, leading to Dirichlet boundary conditions. This provides a natural mechanism for the emergence of D-branes.