Anomalous Supersymmetry

Abstract

We show that supersymmetry is anomalous in $\mathcal{N}=1$ superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic SCFTs at strong coupling. Here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation. The anomaly appears first in four-point functions of two supercurrents with either two R-currents or with an R-current and an energy momentum tensor. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly imply the existence of the anomaly. We outline the implications of this anomaly.

5 pages; v2 - contextual discussion and references added; v3 - final PRL version, with comments added

References in corpus (17)

• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Holographic renormalization and supersymmetry
• Supersymmetry on curved spaces and superconformal anomalies
• Supercurrent anomalies in 4d SCFTs
• Local BRST cohomology in minimal D=4, N=1 supergravity
• Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization
• Anomaly candidates and invariants of D=4, N=1 supergravity theories
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Weyl transformations and trace anomalies in N=1, D=4 supergravities
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• The Holographic Supercurrent Anomaly
• Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere

Cited by in corpus (11)

• Topological Superconductors on Superstring Worldsheets
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
• Comments on Anomalies in Supersymmetric Theories
• Supersymmetry anomalies in new minimal supergravity
• Supersymmetry anomaly in the superconformal Wess-Zumino model
• Consistency of supersymmetric 't Hooft anomalies
• CP-violating supersymmetry anomaly
• Deformations of Supergravity and Supersymmetry Anomalies
• Supersymmetry anomalies and the Wess-Zumino Model in a supergravity background
• Anomalies and Supersymmetry