On Witten’s global anomaly for higher SU(2) representations. (English) Zbl 1006.81079
Summary: The spectral flow of the overlap operator is computed numerically along a particular path in gauge field space. The path connects two gauge equivalent configurations which differ by a gauge transformation in the non-trivial class of \(\pi_4\)(SU(2)). The computation is done with the SU(2) gauge field in the fundamental, the 3/2, and the 5/2 representation. The number of eigenvalue pairs that change places along this path is established for these three representations and an even-odd pattern predicted by Witten is verified.
MSC:
| 81T50 | Anomalies in quantum field theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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