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Non-perturbative Anomalies in $d=2$ QFT

G. Benfatto·P. Falco·V. Mastropietro
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Abstract

We present the first rigorous construction of the QFT Thirring model, for any value of the mass, in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The massless limit is investigated and it is shown that the Schwinger functions have different properties with respect to the ones of the well known exact solution: the Ward Identities have anomalies violating the anomaly non-renormalization property and additional anomalies, apparently unnoticed before, are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.

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G. Benfatto, P. Falco, V. Mastropietro. 2006-07-06. Non-perturbative Anomalies in $d=2$ QFT. https://arxiv.org/abs/hep-th/0607043

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