The Anomaly-Flux-Index Identity and its Euclidean Extension

O'Raifeartaigh, L. (1987) The Anomaly-Flux-Index Identity and its Euclidean Extension. (Preprint)

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The identity of the U(1) anomaly A, the magnetic flux Φ, and the Atiyah-Singer index I (A = Φ = I) for 2n-dimensional compact manifolds is recalled and established in a simple manner by identifying each of them with the central quantity Q = m^2 tr γ(D^2 + m^2)^(-1), where γ is the 2n-dimensional analogue of γ_5, and it is shown that for Euclidean manifolds the identity holds if the index I = (n_+ - n_-) is replaced by the quantity Ĩ = (n_+ - n_-) + (1/π)(η_+(0) - η_-(0)) where η_±(0) are sums over zero-energy phase-shifts.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 20 Jun 2018 11:14
Last Modified: 15 Dec 2022 20:50

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