The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

Supersymmetry anomaly in the superconformal Wess-Zumino model

Supersymmetry anomaly in the superconformal Wess-Zumino model
Supersymmetry anomaly in the superconformal Wess-Zumino model
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.
Anomalies in Field and String Theories, Conformal and W Symmetry, Supergravity Models, Supersymmetry Breaking
1029-8479
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Katsianis, Georgios
ee1fe6fa-951b-498e-b562-7ed6ed8ea4c4
Papadimitriou, Ioannis
61aeb3c8-7ab7-44db-a3ee-846392b997ba
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Katsianis, Georgios
ee1fe6fa-951b-498e-b562-7ed6ed8ea4c4
Papadimitriou, Ioannis
61aeb3c8-7ab7-44db-a3ee-846392b997ba

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]. (doi:10.1007/JHEP02(2021)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
Download (1MB)

More information

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 iD orcid.org/0000-0003-4509-5472
ORCID for Marika Taylor: ORCID iD orcid.org/0000-0001-9956-601X

Catalogue record

Date deposited: 19 Feb 2021 17:32
Last modified: 26 Nov 2021 06:36

Export record

Altmetrics

Contributors

Author: Marika Taylor ORCID iD
Author: Georgios Katsianis
Author: Ioannis Papadimitriou

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×