Supercurves

TL;DR

This work identifies the IIA supercurve as the TST-dual of a general 1/4-supersymmetric D2-brane supertube, recasting it as a string carrying an arbitrary transverse wave moving at speed of light along the T-dual direction. It provides a simple, scale-consistent proof of the classical angular-momentum bound, showing it is saturated by a 1/4-SUSY wave profile known as a superhelix (rank-2 case) and, more generally, by generalized helices determined by the rank of the angular-momentum 2-form; in the quantum theory, the bound is saturated by a unique $SO(8)$ representation, with $J^2=K^2+6K$ and $J\le K$ in the semiclassical limit, where $K$ is tied to the fixed light-cone momentum $|\Delta P_Z|$. The results bridge classical stability arguments for supertubes with perturbative IIA string states, suggesting a unique microstate structure for maximal angular momentum and informing broader questions about the quantum geometry of supersymmetric brane configurations.

Abstract

The TST-dual of the general 1/4-supersymmetric D2-brane supertube is identified as a 1/4-supersymmetric IIA `supercurve': a string with arbitrary transverse displacement travelling at the speed of light. A simple proof is given of the classical upper bound on the angular momentum, which is also recovered as the semi-classical limit of a quantum bound. The classical bound is saturated by a `superhelix', while the quantum bound is saturated by a bosonic oscillator state in a unique SO(8) representation.