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, $hat{n}paralleltextbf{textit{B}}$ and $hat{n}perptextbf{textit{B}}$, 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.
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