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Recent fluorescence spectroscopy experiments on single wall carbon nanotubesreveal substantial deviations of observed absorption and emission energies frompredictions of noninteracting models of the electronic structure. Nonetheless,the data for nearly armchair nanotubes obey a nonlinear scaling relation as afunction the tube radius $R$. We show that these effects can be understood in atheory of large radius tubes, derived from the theory of two dimensionalgraphene where the coulomb interaction leads to a logarithmic correction to theelectronic self energy and marginal Fermi liquid behavior. Interactions onlength scales larger than the tube circumference lead to strong self energy andexcitonic effects that compete and nearly cancel so that the observed opticaltransitions are dominated by the graphene self energy effects.Comment: 4 page

Electron Interactions and Scaling Relations for Optical Excitations in Carbon Nanotubes