  We consider SU(N) symmetric one dimensional quantum chains at finite
temperature. For such systems the correlation lengths, ground state energy, and
excited state energies are investigated in the framework of conformal field
theory. The possibility of different types of excited states are discussed.
Logarithmic corrections to the ground state energy and different types of
excited states in the presence of a marginal opeartor, are calculated. Known
results for SU(2) and SU(4) symmetric systems follow from our general formula.
