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Topological terms and anomaly matching in effective field theories on $\mathbb{R}^3\times S^1$: I. Abelian symmetries and intermediate scales
High Energy Physics - Theory · Submitted 30 Sep 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim While anomaly matching holds as required, it takes a different form than previously thought.
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The abstract, sentence by sentence
We explicitly calculate the topological terms that arise in IR effective field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ by integrating out all but the lightest modes. We then show how these terms match all global-symmetry 't Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-$U(1)$ anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chiral-lagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton 't Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explicitly calculate the topological terms that arise in IR effective field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ by integrating out all but the lightest modes. | contribution 0.75 | 0.96 | 0.11 | asserted 1.00 |
| s1 | We then show how these terms match all global-symmetry 't Hooft anomalies of the UV description. | result 0.83 | 0.95 | 0.36 | asserted 1.00 |
| s2 | We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. | limitation 1.00 | 0.59 | 0.04 | asserted 0.99 |
| s3 | While anomaly matching holds as required, it takes a different form than previously thought. | interpretation 0.63 | 0.79 | 0.30 | asserted 1.00 |
| s4 | For example, cubic- and mixed-$U(1)$ anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chiral-lagrangian Wess-Zumino terms. | result 0.93 | 0.90 | 0.31 | asserted 1.00 |
| s5 | We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton 't Hooft vertices. | contribution 0.96 | 0.94 | 0.09 | asserted 0.99 |
| s6 | We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual. | contribution 0.73 | 0.89 | 0.08 | asserted 0.93 |
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The paper
Original abstract
We explicitly calculate the topological terms that arise in IR effective field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ by integrating out all but the lightest modes. We then show how these terms match all global-symmetry 't Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-$U(1)$ anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chiral-lagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton 't Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.
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References
How the literature uses it
7 arXiv papers cite this in 17 sentences
Papers citing it · 8 sentences without a confident label
Builds on it 2 papers
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Our work uses and generalizes the observation that was first made by Poppitz and Wandler [ref] that cubic- and mixed-$U(1)$ anomalies are matched by local background-field-dependent topological terms instead of chiral-Lagrangian Wess-Zumino-Witten terms, while the $1$-form center symmetry talks directly to the dual photons.
Condensates and anomaly cascade in vector-like theories · Introduction · 0.85
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The answer is that they are matched by a combination of contributions from the massless $λ^I$ fermions and global-symmetry background-field-dependent terms, local in $R^3$, induced upon integrating the non-Cartan and Kaluza-Klein components of all fermions, in a slight generalization of the discussion in [ref] .
Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F) · Symmetry realization, domain walls, and confinement. · 0.96
Uses its method or tool 2 papers
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We adopt the exact same procedure used in [ref] to study the center-symmetry in super Yang-Mills theory.
Condensates and anomaly cascade in vector-like theories · The BC anomaly on $ℝ^3×𝕊^1_L$ · 0.99
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First, we proceed following the recent work [ref] , as it offers the shortest way to our goal.
Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F) · Chiral symmetry breaking on $R^4$ and $R^3 ×S^1$. · 0.96
Compares with it 1 paper
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This is the exact same Lagrangian that was obtained in [ref] for super Yang-Mills theory.
Condensates and anomaly cascade in vector-like theories · The BC anomaly on $ℝ^3×𝕊^1_L$ · 0.92
Cites it as support 1 paper
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The spontaneous breaking of parity at $θ=π$ in pure $SU(N)$ gauge theory is borne out by older large-$N$ [ref] and other arguments, reviewed in [ref] , and by explicit semiclassical calculations[The results reported in this paper also originate from work on extensions of our recent study [ref] of anomalies in the calculable $^3 ×^1$ framework.] on $^3 ×^1$ from the past decade [ref] .
The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles · Introduction: motivation and a brief description · 0.98
Cites it as background 2 papers
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The higher-form anomalies, anomalies associated with higher-form symmetries, were taken seriously by many authors, which led to a plethora of papers that examined different aspects of QFT (see [ref] for a non-comprehensive list).
New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories · Introduction and Summary · 0.95
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For a recent discussion of these symmetries see also [ref] .
Confinement on $\mathbb{R}^3 \times \mathbb{S}^1$ and Double-String Collapse · Symmetries and Vacua · 0.98
What it cites · 62 sentences without a confident label
Uses the method or tool of 4 papers
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We follow the formalism of [ref] and the recent work on gauging center symmetry in dYM [ref] .
Coupling a QFT to a TQFT and Duality · Turning on background gauge fields for the center and chiral symmetries · 0.95
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We follow the formalism of [ref] and the recent work on gauging center symmetry in dYM [ref] .
Modified instanton sum in QCD and higher-groups · Turning on background gauge fields for the center and chiral symmetries · 0.95
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This makes the first infinite sum easier to evaluate; one can show that:[This was used in [ref] .
Chiral anomalies on a circle and their cancellation in F-theory · The BF term · 0.95
Compares with 6 papers
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The advantage of ([ref]) is that it is valid throughout the RG flow and does not require an embedding of $_N^(1)$ in the emergent center symmetry, as in [ref] .
Modified instanton sum in QCD and higher-groups · Turning on background gauge fields for the center and chiral symmetries · 0.85
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The advantage of ([ref]) is that it is valid throughout the RG flow and does not require an embedding of $_N^(1)$ in the emergent center symmetry, as in [ref] .
Anomalies in the Space of Coupling Constants and Their Dynamical Applications II · Turning on background gauge fields for the center and chiral symmetries · 0.85
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Explicitly, the definition of $ϕ⃗$, relating it to $A⃗_3$, is[ Notice that, compared to most previous work on the subject, $2 πϕ⃗|_this paper = ϕ⃗|_older refs.$, e.g. [ref] .] [equation] Here $ρ⃗$ is the Weyl vector.
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects · Dynamical fields, scales, and center symmetries in the Coulomb branch EFT · 0.96
Cites as background 22 papers
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The action of the global $_N^(1)$ and $_N^^1$ 1-form and 0-form center symmetries was discussed in Section [ref], in a manner that used an embedding of these symmetries into the $U(1)^N-1$ emergent center symmetry of the Coulomb-branch EFT, used earlier in [ref] .
Modified instanton sum in QCD and higher-groups · Turning on background gauge fields for the center and chiral symmetries · 0.90
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The action of the global $_N^(1)$ and $_N^^1$ 1-form and 0-form center symmetries was discussed in Section [ref], in a manner that used an embedding of these symmetries into the $U(1)^N-1$ emergent center symmetry of the Coulomb-branch EFT, used earlier in [ref] .
Anomalies in the Space of Coupling Constants and Their Dynamical Applications II · Turning on background gauge fields for the center and chiral symmetries · 0.90
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On $^4$ (see e.g. [ref] for reviews), the theory is known to break $_2N^(0) →_2^(0)$ and have $N$ vacua with domain walls (DW) between them.
Lectures on supersymmetric gauge theories and electric-magnetic duality · The scope and main results of this paper · 0.93
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