Boundary CFT Construction of D-branes in Vacuum String Field Theory

TL;DR

The authors extend vacuum string field theory to general D-brane configurations in a fixed 26D BCFT background by exploiting the sliver surface state as a universal BCFT construct. They show that D-brane tensions are encoded by disk partition functions and construct brane solutions for arbitrary BCFTs via boundary condition changing elements, enabling multi-brane and coincident-brane configurations. Finite and small deformations of the sliver are analyzed as boundary RG flows and marginal perturbations, connecting to a theory-space covariant framework that formalizes background independence. The paper also develops a program to identify the physical open string spectrum around a D-brane background through a factorization ansatz and deformed projectors, while acknowledging unresolved issues in the ghost sector and the precise spectrum. Overall, vacuum SFT provides an analytic, background-independent mechanism for constructing D-branes and exploring their moduli and excitations via BCFT techniques.

Abstract

In previous papers we built (multiple) D-branes in flat space-time as classical solutions of the string field theory based on the tachyon vacuum. In this paper we construct classical solutions describing all D-branes in any fixed space-time background defined by a two-dimensional CFT of central charge 26. A key role is played by the geometrical definition of the sliver state in general boundary CFT's. The correct values for ratios of D-brane tensions arise because the norm of the sliver solution is naturally related to the disk partition function of the appropriate boundary CFT. We also explore the possibility of reproducing the known spectrum of physical states on a D-brane as deformations of the sliver.

Figures (10)

• Figure 1: A punctured disk $D$ with a local coordinate around the puncture $P$. The coordinate is defined through a map $m$ from a canonical half disk $H_U$ to the disk. The arcs $AM$ and $MB$ in $D$ represent the left half and the right half of the open string respectively.
• Figure 2: Three canonical presentations of the disk $D$. (b) Disk presented as the unit disk $D_0$ with global coordinate $w$. (c) Disk presented as the upper half plane $D_H$ with global coordinate $z$. (d) Disk presented as $\widehat{D}$ with global coordinate $\widehat{w}$. Here the image of $H_U$ is also a half-disk.
• Figure 3: The definition of wedge states for arbitrary $n$. (a) The canonical half disk $H_U$. (b) The map of $H_U$ into a vertical half-disk. (c) The inclusion of the vertical half-disk of (b) into the disk $D_0$ with global coordinate $w$. (d) The map of $D_0$ into the upper half plane $D_H$.
• Figure 4: (a) The surface state corresponding to the identity string field $\langle{\cal I}|$. Here the image of $H_U$ covers the full disk, except for a cut in the negative real axis. (b) The surfaces state corresponding to the sliver $\langle \Xi|$. Here the image of $H_U$ covers an infinitesimally thin sliver around the positive real axis.
• Figure 5: Using $\widehat{w}$ global coordinates the sliver appears as a cone with infinite excess angle-- namely, an infinite helix. The segments $AM$ and $BM$ represent the left-half and the right-half of the string. The local coordinate patch, represented by the shaded half disk shown to the right, must be glued in to form the complete surface.