  We predict properties of triplet excited states in single-walled carbon
nanotubes (CNTs) using a time-dependent density-functional theory (TD-DFT). We
show that the lowest triplet state energy in CNTs to be about 0.2-0.3 eV lower
than the lowest singlet states. Like in $\pi$-conjugated polymers, the lowest
CNT triplets are spatially localized. These states show strong optical
absorption at about 0.5-0.6 eV to the higher lying delocalized triplet states.
These results demonstrate striking similarity of the electronic features
between CNTs and $\pi$-conjugated polymers and provide explicit guidelines for
spectroscopic detection of CNT triplet states.
