  We have investigated excitons in highly-aligned single-walled carbon
nanotubes (SWCNTs) through optical spectroscopy at low temperature (1.5 K) and
high magnetic fields ($\textbf{\textit{B}}$) up to 55 T. SWCNT/polyacrylic acid
films were stretched, giving SWCNTs that are highly aligned along the direction
of stretch ($\hat{n}$). Utilizing two well-defined measurement geometries,
$\hat{n}\parallel\textbf{\textit{B}}$ and $\hat{n}\perp\textbf{\textit{B}}$, we
provide unambiguous evidence that the photoluminescence energy and intensity
are only sensitive to the $\textbf{\textit{B}}$-component parallel to the tube
axis. A theoretical model of one-dimensional magneto-excitons, based on
exchange-split `bright' and `dark' exciton bands with
Aharonov-Bohm-phase-dependent energies, masses, and oscillator strengths,
successfully reproduces our observations and allows determination of the
splitting between the two bands as $\sim4.8$ meV for (6,5) SWCNTs.
