Nonabelian chiral anomaly and the spin gap in one-dimensional interacting electron systems

We critically examine the issue raised by Nagaosa and Oshikawa [J. Phys. Sec. Jpn. 65 (1996) 2241] on how Fujikawa's Jacobian arising from chiral anomaly contributes a topological term to the derivative expansion of the Id Hubbard model at half filling, thus governing the behaviour of the spin gap. We find that when the nonabelian nature of the system is properly accounted for, the scheme requires modification. The modified result is shown to agree with nonabelian bosonization. Extensions to spin-Peierls systems are outlined.