  Recently, B. Gerganov, A. LeClair and M. Moriconi [Phys. Rev. Lett. 86 (2001)
4753] have proposed an "exact" (all orders) beta-function for 2-dimensional
conformal field theories with Kac-Moody current-algebra symmetry at any level
k, based on a Lie group G, which are perturbed by a current-current
interaction. This theory is also known as the Non-Abelian Thirring model. We
check this conjecture with an explicit calculation of the beta-function to
4-loop order, for the classical groups G= SU(N), SO(N) and SP(N). We find a
contribution at 4-loop order, proportional to a higher-order group-theoretical
invariant, which is incompatible with the proposed beta-function in all
possible regularization schemes.
