  We present a quantitative theory of optical absorption polarized transverse
to the tube axes in semiconducting single-walled carbon nanotubes. Transverse
optical absorption in semiconducting single-walled carbon nanotubes is to an
exciton state that is strongly blueshifted, relative to the two lowest
longitudinal excitons, by electron-electron interactions. The binding energy of
the transverse exciton is considerably smaller than those of the longitudinal
excitons. Electron-electron interactions also reduce the relative oscillator
strength of the transverse optical absorption. Our theoretical results are in
excellent agreement with recent experimental measurements in four chiral
nanotubes.
