  Recent fluorescence spectroscopy experiments on single wall carbon nanotubes
reveal substantial deviations of observed absorption and emission energies from
predictions of noninteracting models of the electronic structure. Nonetheless,
the data for nearly armchair nanotubes obey a nonlinear scaling relation as a
function the tube radius $R$. We show that these effects can be understood in a
theory of large radius tubes, derived from the theory of two dimensional
graphene where the coulomb interaction leads to a logarithmic correction to the
electronic self energy and marginal Fermi liquid behavior. Interactions on
length scales larger than the tube circumference lead to strong self energy and
excitonic effects that compete and nearly cancel so that the observed optical
transitions are dominated by the graphene self energy effects.
