On the Moduli Space of the Localized 1-5 System

TL;DR

This paper computes the moduli space metric for localized 1- and 5-branes with momentum, revealing new features and differences from delocalized cases, which may aid in understanding BPS bound states.

Contribution

It introduces a detailed calculation of the moduli space for localized 1-5 branes with momentum, highlighting differences from delocalized configurations and implications for BPS states.

Findings

Moduli space metric differs significantly from delocalized case when both charges are localized.

New moduli associated with 1-brane motion along 5-branes are identified.

Results depend on torus size, with finite contributions as size goes to infinity.

Abstract

We calculate the effective action for small velocity scattering of localized 1-branes and 5-branes. Momentum is allowed to flow in the direction along the 1-branes so that the moduli space has only 1/8 of the full supersymmetry. Relative to the more familiar case with the 1-branes delocalized along the 5-branes, this introduces new moduli associated with the motion of the 1-branes along the 5-branes. We consider in detail the moduli space metric for the associated two body problem. Even for motion transverse to the 5-brane, our results differ substantially from the delocalized case. However, this difference only appears when both the 1-brane charge and the momentum charge are localized. Despite the fact that, in a certain sense, 1-branes spontaneously delocalize near a 5-brane horizon, the moduli space metric in this limit continues to differ from the delocalized result. This fact may be of use in developing a new description of the associated BPS bound states. The new terms depend on the torus size $L$ in such a way that they give a finite contribution in the $L \to \infty$ limit.