U(1) Anomaly and Index Theorem for Complex and Euclidean Manifolds

O'Raifeartaigh, L. (1987) U(1) Anomaly and Index Theorem for Complex and Euclidean Manifolds. (Preprint)

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Abstract

It is shown that the usual U(1)-anomaly for D exists for any supersymmetric (QM) operator Δ, and that it is the value at the origin of the Laplace transform of the supersymmetric partition function Z(t) (in contrast to the η-invariant which is the value at the origin of the Mellin transform of Z(t)). The known equality of the anomaly A, the flux Φ, and the AS-index I for compact manifolds without boundaries is generalised to the case of Euclidean manifolds, where the fractional discrepancy between A=Φ and I is shown to be a sum over zero-energy phase-shifts (of the Bohm-Aharonov type). The relationship between the results for Euclidean manifolds and compact manifolds with boundaries is illustrated by using as an example the 2-dimensional Dirac operator.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 10 Jul 2018 14:57
Last Modified: 23 Jul 2018 14:20
URI: http://dair.dias.ie/id/eprint/905

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