On Witten's global anomaly for higher SU(2) representations

TL;DR

This paper numerically investigates Witten's global anomaly for higher SU(2) representations by computing the spectral flow of the overlap operator, confirming some predicted patterns but revealing more complex behaviors.

Contribution

It provides the first numerical verification of Witten's global anomaly for SU(2) in higher representations, highlighting unexpected complexities.

Findings

Confirmed the even-odd spectral flow pattern for 3/2 and 5/2 representations

Revealed more intricate spectral flow behavior than previously expected

Validated the theoretical predictions with numerical evidence

Abstract

The spectral flow of the overlap operator is computed numerically along a path connecting two gauge fields which differ by a topologically non-trivial gauge transformation. The calculation is performed for SU(2) in the 3/2 and 5/2 representation. An even-odd pattern for the spectral flow as predicted by Witten is verified. The results are, however, more complicated than naively expected.