Talk presented by Oliver Baer

Parallel Session: Chiral Gauge Theories

Thursday July 1st, 15.10 - 15.30, Room 8

Witten's SU(2) anomaly and spectral flow of Neuberger's operator

Abstract: Based on the Ginsparg-Wilson relation some progress has been achieved in formulating chiral gauge theories on the lattice. As first realized by Witten, a SU(2) theory with a single Weyl fermion is afflicted with a global anomaly. The anomaly is closely related to the spectral flow of the Dirac operator. Following Witten's reasoning we computed numerically the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation. As expected, the lowest eigenvalue crosses zero. Subsequently there exist closed loops in configuration space where the fermion detereminant changes its sign.

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