Aspects of supertubes

TL;DR

This work analyzes supersymmetric supertubes ending on a D4-brane and their higher-dimensional extensions. It constructs explicit D4 BI solutions describing D2 supertubes ending on arbitrary curves, derives the full nonlinear BI equations, and shows the configurations preserve $1/8$ of supersymmetry, with the energy decomposing into D4-brane and supertube contributions. It further explores D4- and D3-tube generalizations via T-duality, highlighting stability in non-supersymmetric cases and signaling divergences from infinite D2 components which compactification can address. The open-string perspective reveals that open-string boundary couplings on a supertube remain conformal to all orders in $\alpha'$, thanks to the open-string metric rendering the cross-section coordinate $\phi$ effectively null ( $\langle\phi\phi\rangle=0$ ), thereby preserving the arbitrary cross-section profile at the string level. Collectively, these results illuminate how brane intersections stabilize via worldvolume fluxes, extend the supertube paradigm to curved geometries, and offer a robust string-theoretic description of these dyonic configurations with potential holographic and gauge-theory applications.

Abstract

We find supersymmetric solutions of the D4 brane Born-Infeld action describing D2 supertubes ending on an arbitrary curve inside a D4 brane. From the D4 brane point of view, these are dyonic strings. We also consider various higher dimensional extensions of the usual supertubes, involving expanded D4 and D3 brane configurations. Finally, considering the worldsheet theory for open strings on a supertube, we show that this configuration is an exact solution to all orders in alpha'. Further the causal structure of the open-string metric provides new insight into the arbitrary cross-section of the supertube solutions. From this point of view, it is similar to the arbitrary profile that appears for certain null plane waves.