  We show that the optical absorption spectra of boron nitride (BN) nanotubes
are dominated by strongly bound excitons. Our first-principles calculations
indicate that the binding energy for the first and dominant excitonic peak
depends sensitively on the dimensionality of the system, varying from 0.7 eV in
bulk hexagonal BN via 2.1 eV in the single sheet of BN to more than 3 eV in the
hypothetical (2,2) tube. The strongly localized nature of this exciton dictates
the fast convergence of its binding energy with increasing tube diameter
towards the sheet value. The absolute position of the first excitonic peak is
almost independent of the tube radius and system dimensionality. This provides
an explanation for the observed "optical gap" constancy for different tubes and
bulk hBN [R. Arenal et al., to appear in Phys. Rev. Lett. (2005)].
