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Comments on chiral algebras and $\Omega$-deformations
High Energy Physics - Theory · Submitted 5 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We provide an alternative construction of this chiral algebra by performing an $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on $\mathbf{R}^6$ and restricting to the cohomology of a specific supercharge.
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Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. We provide an alternative construction of this chiral algebra by performing an $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on $\mathbf{R}^6$ and restricting to the cohomology of a specific supercharge. In addition, we show that the central charge of the chiral algebra can be obtained by performing equivariant integration of the anomaly polynomial of the six-dimensional theory. Furthermore, we generalize this construction to include orbifolds of the $\mathbf{R}^4$ transverse to the chiral algebra plane.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. | background 0.99 | 0.11 | 0.29 | asserted 1.00 |
| s1 | We provide an alternative construction of this chiral algebra by performing an $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on $\mathbf{R}^6$ and restricting to the cohomology of a specific supercharge. | contribution 0.51 | 0.95 | 0.24 | asserted 1.00 |
| s2 | In addition, we show that the central charge of the chiral algebra can be obtained by performing equivariant integration of the anomaly polynomial of the six-dimensional theory. | result 0.78 | 0.92 | 0.17 | asserted 1.00 |
| s3 | Furthermore, we generalize this construction to include orbifolds of the $\mathbf{R}^4$ transverse to the chiral algebra plane. | contribution 0.99 | 0.92 | 0.09 | asserted 1.00 |
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The paper
Original abstract
Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. We provide an alternative construction of this chiral algebra by performing an $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on $\mathbf{R}^6$ and restricting to the cohomology of a specific supercharge. In addition, we show that the central charge of the chiral algebra can be obtained by performing equivariant integration of the anomaly polynomial of the six-dimensional theory. Furthermore, we generalize this construction to include orbifolds of the $\mathbf{R}^4$ transverse to the chiral algebra plane.
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How the literature uses it
6 arXiv papers cite this in 6 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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Indeed already in six-dimensions there might be a a natural relation to the the chiral algebra studied in [ref]
Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions · Conclusion · 0.95
Cites it as background 1 paper
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There are some examples: supersymmetric CFTs in $d=3$, $4$, and $6$, with at least 8 real supercharges, have a subsector described by a chiral algebra [ref] .
Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual · 1. Introduction · 0.81
What it cites · 118 sentences without a confident label
Builds on 4 papers
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The chiral algebra construction of [ref] can be applied also to 2d SCFTs with $𝒩=(0,4)$ supersymmetry.
Infinite Chiral Symmetry in Four Dimensions · 2d $𝒩=(0,4)$ SCFTs and chiral algebras · 0.93
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As discussed in Section [ref], we can generalize the setup of [ref] and replace $Σ= 𝐑^2$ and $X_4 = 𝐑^4$ by the orbifold spaces $𝐂/𝐙_k$ and $𝐂^2/𝐙_k$ where the orbifold action is $z ↦^2πi / k z$ and $(z,w)↦(^2πi / k z,^-2πi / k w)$, respectively.
W Symmetry in six dimensions · Including orbifolds · 0.98
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Similarly, it is possible to generalize the four-dimensional construction of [ref] to include an Abelian orbifold of the plane transverse to the chiral algebra plane, i.e. take $Σ= 𝐑^2/𝐙_k$ as the surface transverse to $C$.
Chiral algebras from \Omega-deformation · Orbifolds and defects · 0.98
Uses the method or tool of 8 papers
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In terms of the 4d $𝒩=2$ supercurrents we can define the $Ω$-deformed twisted supercharge as $Q_Ω= Q+ ι_V G$, where $Q$ is the scalar supercharge of the four-dimensional topological-holomorphic twist of [ref] and $G$ is a one-form supercharge associated to the same twist.
Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality · $Ω$-deformation of the Kapustin twist · 0.81
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To answer the dynamical question of the precise form of the chiral algebra one may adopt the approach followed in [ref] which, in short, amounts to an educated guess supported by highly non-trivial consistency checks.
W Symmetry in six dimensions · Comments on supersymmetric localization · 0.86
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Next, following [ref] , we want to define special nilpotent supercharges $Q$ which commute with the generators $L_0,L_±1$ and for which the anti-holomorphic transformations are $Q$-exact.
Infinite Chiral Symmetry in Four Dimensions · No new chiral algebras in 2d · 0.91
Compares with 9 papers
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We then show that this is precisely the same supercharge as the one used in the chiral algebra construction of [ref] establishing an equivalence between the two chiral algebras.
W Symmetry in six dimensions · Introduction · 0.94
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These are precisely the chiral algebra anomalies derived by different methods in [ref] .
Infinite Chiral Symmetry in Four Dimensions · Chiral algebras in 4d $=2$ SCFTs · 0.95
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Our construction is similar in spirit to the one in [ref] which is relevant for the chiral algebras associated with 4d $=2$ SCFTs.
Chiral algebras from \Omega-deformation · Discussion · 0.93
Cites as background 23 papers
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In the construction of [ref] the chiral algebra in [ref] is derived by employing the topological-holomorphic twist of Kapustin [ref] on $Σ×C$ such that the theory is topological on $Σ$ and holomorphic on $C$.
SCFT/VOA correspondence via $\Omega$-deformation · $Ω$-deformation of the Kapustin twist · 0.80
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In the construction of [ref] the chiral algebra in [ref] is derived by employing the topological-holomorphic twist of Kapustin [ref] on $Σ×C$ such that the theory is topological on $Σ$ and holomorphic on $C$.
Infinite Chiral Symmetry in Four Dimensions · $Ω$-deformation of the Kapustin twist · 0.80
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In the construction of [ref] the chiral algebra in [ref] is derived by employing the topological-holomorphic twist of Kapustin [ref] on $Σ×C$ such that the theory is topological on $Σ$ and holomorphic on $C$.
Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality · $Ω$-deformation of the Kapustin twist · 0.80
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