THE SU(2) GLOBAL ANOMALY THROUGH LEVEL CIRCLING
Minos Axenides, HOLGER BECH NIELSEN, Andrei Johansen · Modern Physics Letters A · 1994
We discuss a novel manifestation of the SU(2) global anomaly in an SU(2) gauge theorywith an odd number of chiral quark doublets and arbitrary Yukawa couplings. We arguethat the massive four-dimensional Euclidean Dirac operator is non-Hermitian with itsspectrum of eigenvalues (λ, −λ) lying in pairs in the complex plane. Consequently theexistence of an odd number of normalizable zero modes of the four-dimensional massiveDirac operator is equivalent to a fermionic level exchange phenomenon, level “circling,”under continuous topologically non-trivial deformations of the external gauge field. Moregenerally global anomalies are a manifestation of fermionic level “circling” in any SP(2n)gauge theory with an odd number of massive fermions in the spinor representation andarbitrary Yukawa couplings.