Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Masaki Okada, Masaki Okada, , ,
| Summary:
We point out that fermionic unitary operators which anticommute among
themselves appear in various situations in quantum field theories with
anomalies in the Hamiltonian formalism. To illustrate, we give multiple
derivations of the fact that position-dependent $U(1)$ transformations of
two-dimensional theories with $U(1)$ symmetry of odd level are fermionic when
the winding number is odd. We then relate this mechanism to the anomalies of
the discrete $mathbbZ_N subset U(1)$ symmetry, whose description also
crucially uses unitary operators which are fermionic. We also show that
position-dependent $SU(2)$ transformations of four-dimensional theories with
$SU(2)$ symmetry with Witten anomaly are fermionic and anticommute among
themselves when the winding number is odd.
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