Microscopic string analysis of the D0-D8 brane system and dual R-R states

TL;DR

This work provides a microscopic, local account of RR forces in D-brane systems, focusing on the D0–D8 configuration. By employing boundary-state formalism and constructing BRST-invariant RR vertex operators in an asymmetric picture, it shows that RR exchanges are mediated by RR potentials related by duality, not merely by field strengths. The analysis reveals a two-dimensional RR Hilbert space with degenerate metric, yielding null states and enabling the identification of RR potentials that couple to both branes in the ν=8 case, thus delivering a Coulomb-like interpretation of the RR interaction and resolving the microscopic puzzle of string creation via duality. The results bridge string-theoretic amplitudes with their supergravity counterparts, clarifying how dual RR charges govern brane interactions and the conditions under which no net force arises.

Abstract

Using the boundary state formalism, we perform a microscopic string analysis of the interaction between two D-branes and provide a local interpretation for the R-R force in the D0-D8 brane system. To do so, we construct BRST invariant vertex operators for the massless R-R states in the asymmetric picture that are proportional to potentials rather than field strengths. The Hilbert space of such R-R states contains combinations of two vectors that decouple from all physical amplitudes, even in the presence of boundaries. Identifying these vectors, we remove the null states and recover duality relations among R-R potentials. If we specify to the D0-D8 brane system, this mechanism implies that the R-R 1-form state has a non-zero overlap with both the D0-brane and the D8-brane, thus explaining from a local point of view the non-vanishing R-R contribution in the interaction for the D0-D8 brane system and those related to it by duality.