Supertubes and Supercurves from M-Ribbons

TL;DR

The paper constructs 1/4 BPS M-ribbon configurations of M2-branes on T^2 that reproduce the known type IIA objects, supertubes and supercurves, upon dimensional reduction. It advances a covariant SL(2,Z) generalization that channels these ribbons into an SL(2,Z) family of dual configurations, including an IIB interpretation as (n,m)-strings with momentum and a special case as the super D-helix. The authors derive explicit BPS bounds and show the energy decomposes into familiar charges (D0, F1) and, in the SL(2,Z) generalization, into (mq−np) strings wrapped with momentum, while enforcing a straightness condition in one direction. The work provides a coherent M-theory framework linking M2-brane ribbons, their IIA reductions, and dual IIB pictures, clarifying stability, duality relations, and constraints on deformations of these 1/4 BPS configurations.

Abstract

We construct 1/4 BPS configurations, `M-ribbons', in M-theory on T^2, which give the supertubes and supercurves in type IIA theory upon dimensional reduction. These M-ribbons are generalized so as to be consistent with the SL(2,Z) modular transformation on T^2. In terms of the type IIB theory, the generalized M-ribbons are interpreted as an SL(2,Z) duality family of super D-helix. It is also shown that the BPS M-ribbons must be straight in one direction.

Figures (1)

• Figure 1: (a) M-ribbon wrapped around the 11th dimension, is equivalent to the supertube when the 11th dimension is reduced, and (b) to supercurve. They transform into each other under 9-11 flip.