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تسجيل مستخدم جديدOn Wittens global anomaly for higher SU(2) representations
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O. Baer
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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.
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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.
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