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Supersymmetry anomaly in the superconformal Wess-Zumino model

Skenderis, Kostas, Taylor, Marika, Katsianis, Georgios and Papadimitriou, Ioannis (2021) Supersymmetry anomaly in the superconformal Wess-Zumino model. Journal of High Energy Physics, 2021 (2), [209].

Record type: Article

Abstract

We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-loop computation using a supersymmetric Pauli-Villars regulator.

The conformal current multiplet does not exist in the regulated theory because the regulator breaks conformal invariance, R-symmetry and S-supersymmetry explicitly. The minimal massive multiplet is the Ferrara-Zumino (FZ) one and the supersymmetry preserved by the regulator is a specific field dependent combination of Q- and S- supersymmetry of the conformal multiplet. While this supersymmetry is non anomalous, conformal invariance, R-symmetry and the original Q- and S-supersymmetries are explicitly broken by finite contact terms, both in the regulated and renormalized theories.

A conformal current multiplet does exist for the renormalized theory and may be obtained from the FZ multiplet by a set of finite local counterterms that eliminate the explicit symmetry breaking, thus restoring superconformal invariance up to anomalies. However, this necessarily renders both Q- and S-supersymmetries anomalous, as is manifest starting at 4-point functions of conformal multiplet currents. The paper contains a detailed discussion of a number of issues and subtleties related to Ward identities that may be useful in a wider context.

Text
SAWZv15JHEPr1 - Accepted Manuscript

Accepted/In Press date: 31 January 2021
e-pub ahead of print date: 24 February 2021
Keywords: Anomalies in Field and String Theories, Conformal and W Symmetry, Supergravity Models, Supersymmetry Breaking

Identifiers

Local EPrints ID: 446742
URI: http://eprints.soton.ac.uk/id/eprint/446742
ISSN: 1029-8479
PURE UUID: fe1aa552-eceb-465d-b5de-d1f18dde6aef
ORCID for Kostas Skenderis: orcid.org/0000-0003-4509-5472
ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

Catalogue record

Date deposited: 19 Feb 2021 17:32

Contributors

Author: Marika Taylor
Author: Georgios Katsianis