On Least Action D-Branes

TL;DR

The paper investigates how relevant boundary terms shape D-brane configurations in bosonic string theories with toroidal and orbifold compactifications. It develops a boundary-entropy ($g$-factor) framework, computing exact $g$ for Neumann and Dirichlet boundary conditions across $c=1$ and general toroidal backgrounds, and analyzes how T-duality and orbifold structure constrain brane stability. Key results include explicit $g$ expressions for circle and torus compactifications, orbifold relations, Ginsparg points with enhanced symmetry, and a general treatment of mixed Dirichlet/Neumann boundaries showing $g_k$ depends only on tangent $B$-field components. The findings provide a least-action perspective on brane stability across moduli space, linking boundary RG flows to duality orbits and clarifying when Neumann or Dirichlet conditions dominate. Overall, the work offers a concrete, duality-consistent map of stable boundary conditions in bosonic string compactifications with boundaries.

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.

Figures (2)

• Figure 1: Map of the preferred boundary conditions in the $c=1$ moduli space
• Figure 2: Map of the prefered boundary conditions in $c=2$ moduli space. The hyper plane $\rho_{2}=\tau_{2}$ is denoted in black. The grey figure below, marked by the vertical lines, is the cylinder $\rho_{1}^{2}+\rho_{2}^{2}=1/4$. The curved surface above is the hypersurface $\rho_{1}^{2}+\rho_{2}^{2}=\rho_{2}/4\tau_{2}$. In the region between the hypersurface and the hyperplane the least value for the entropy is provided by $g_{DN}$, between the cylinder and the hyperplane by $g_{DD}$, and inside of the cylinder and below the hypersurface by $g_{NN}$.