  We demonstrate that a non-perturbative framework for the treatment of the
excitations of single walled carbon nanotubes based upon a field theoretic
reduction is able to accurately describe experiment observations of the
absolute values of excitonic energies. This theoretical framework yields a
simple scaling function from which the excitonic energies can be read off. This
scaling function is primarily determined by a single parameter, the charge
Luttinger parameter of the tube, which is in turn a function of the tube
chirality, dielectric environment, and the tube's dimensions, thus expressing
disparate influences on the excitonic energies in a unified fashion. We test
this theory explicitly on the data reported in NanoLetters 5, 2314 (2005) and
Phys. Rev. B. 82, 195424 (2010) and so demonstrate the method works over a wide
range of reported excitonic spectra.
