On Least Action D-Branes

TL;DR

This paper investigates how boundary terms influence brane stability and boundary conditions in bosonic string compactifications, revealing how moduli space regions and T-duality shape brane configurations.

Contribution

It introduces a least-action approach to analyze boundary conditions, uncovering stability regions and the limited role of the B-field in Dirichlet branes.

Findings

Neumann conditions dominate at small radii

Dirichlet conditions dominate at large radii

T-duality points are special in moduli space

Abstract

We discuss the effect of relevant boundary terms on the nature of branes. This is done for toroidal and orbifold compactifications of the bosonic string. Using the relative minimalization of the boundary entropy as a guiding principle, we uncover the more stable boundary conditions at different regions of moduli space. In some cases, Neumann boundary conditions dominate for small radii while Dirichlet boundary conditions dominate for large radii. The c=1 and c=2 moduli spaces are studied in some detail. The antisymmetric background field B is found to have a more limited role in the case of Dirichlet boundary conditions. This is due to some topological considerations. The results are subjected to T-duality tests and the special role of the points in moduli space fixed under T-duality is explained from least-action considerations.