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Anomalous Supersymmetry
High Energy Physics - Theory · Submitted 18 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that supersymmetry is anomalous in ${\cal N}=1$ superconformal quantum field theories (SCFTs) with an anomalous R-symmetry.
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The abstract, sentence by sentence
We show that supersymmetry is anomalous in ${\cal N}=1$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that supersymmetry is anomalous in ${\cal N}=1$ superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. | result 0.87 | 0.94 | 0.94 | asserted 1.00 |
| s1 | This anomaly was originally found in holographic SCFTs at strong coupling. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s2 | 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. | contribution 0.97 | 0.96 | 0.32 | asserted 1.00 |
| s3 | 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. | result 0.99 | 0.68 | 0.12 | asserted 1.00 |
| s4 | In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly imply the existence of the anomaly. | result 0.74 | 0.54 | 0.15 | asserted 1.00 |
| s5 | We outline the implications of this anomaly. | interpretation 0.86 | 0.63 | 0.04 | unclear 0.80 |
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The paper
Original abstract
We show that supersymmetry is anomalous in ${\cal N}=1$ 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.
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References
How the literature uses it
14 arXiv papers cite this in 28 sentences
Papers citing it · 21 sentences without a confident label
Compares with it 1 paper
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While the existence of a finite counterterm $𝒲_fin$ does not contradict the results of [ref] , it may be in agreement with the superspace analysis in [ref] .
Supersymmetry anomaly in the superconformal Wess-Zumino model · Finite counterterm and the Ward identities for the conformal multiplet · 0.90
Cites it as background 5 papers
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Correlation functions and (anomalous) Ward-Takahashi identities have been revisited in perturbation theories [ref] .
CP-violating supersymmetry anomaly · Introduction · 0.80
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These quantum corrections to supersymmetric Ward identities, also referred to as “supersymmetry anomalies,” were studied long ago in [ref] , and more recently in [ref] .
't Hooft anomalies and the holomorphy of supersymmetric partition functions · Introduction · 0.95
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More recently this question has attracted renewed interest, starting from some explicit computations that described anomalous supersymmetric Ward identities for 4-dimensional supersymmetric matter quantum field theories (SQFT's) with anomalous R symmetry [ref] .
Deformations of Supergravity and Supersymmetry Anomalies · Introduction and summary · 0.86
What it cites · 19 sentences without a confident label
Contests 2 papers
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Early attempts to compute the supertrace Ward identity can be found in [ref] but these missed contributions to the anomaly involving the R-symmetry current and the Ricci tensor.
The Holographic Supercurrent Anomaly · Introduction · contest 0.82
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Early attempts to compute the supertrace Ward identity can be found in [ref] but these missed contributions to the anomaly involving the R-symmetry current and the Ricci tensor.
Superconformal Anomaly from AdS/CFT Correspondence · Introduction · contest 0.82
Compares with 3 papers
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However, as noted earlier, there are important differences in the physics (in [ref] the gauge anomalies must vanish for consistency of the model, while this is not so for the R-anomalies relevant for us), as well as in the context (the WZ conditions discussed in [ref] are for a vector multiplet in flat space, while the anomalies in Table [ref] are those of $=1$ conformal supergravity [ref] ).
Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity · Introduction · 0.99
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The anomalies of the bosonic currents are in agreement with the results derived in [ref] .
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories · Introduction · 0.99
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The anomalies of the bosonic currents are in agreement with the results derived in [ref] .
Supersymmetry on curved spaces and superconformal anomalies · Introduction · 0.99
Cites as support 1 paper
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This argument does not rely on the theory having conformal invariance, and thus we expect any 4d supersymmetric theory with an R-symmetry anomaly to have a corresponding anomaly in the conservation of the supercurrent.[This expectation has been verified in the followup paper [ref] .]
Supersymmetry anomalies in new minimal supergravity · Introduction · 1.00
Cites as background 7 papers
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The full superconformal anomalies for the $=1$ current multiplet were computed holographically in [ref] , while [ref] obtained the superconformal anomalies in the presence of local supersymmetric scalar couplings.
Supercurrent anomalies in 4d SCFTs · Introduction · 0.82
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The full superconformal anomalies for the $=1$ current multiplet were computed holographically in [ref] , while [ref] obtained the superconformal anomalies in the presence of local supersymmetric scalar couplings.
Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization · Introduction · 0.82
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It was realised early on [ref] that one cannot maintain at the quantum level simultaneously $∂^μQ_μ=0$ and $γ^μQ_μ=0$ and, if the model is a gauge theory, gauge invariance: one of the three conditions must be relaxed and the standard choice is to have a superconformal anomaly.
4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow · Introduction · 0.92
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