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Effective Gravitational Couplings of Kaluza-Klein Gauge Theories
High Energy Physics - Theory · Submitted 8 Jun 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.
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We study the effective gravitational couplings of four-dimensional Kaluza-Klein compactified gauge theories with eight supercharges. The class of theories we consider are the pure SU(N) Yang-Mills theories at admissible Chern-Simons levels and the conformal gauge theories with 2N fundamental flavours. The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the effective gravitational couplings of four-dimensional Kaluza-Klein compactified gauge theories with eight supercharges. | contribution 0.99 | 0.89 | 0.05 | asserted 0.79 |
| s1 | The class of theories we consider are the pure SU(N) Yang-Mills theories at admissible Chern-Simons levels and the conformal gauge theories with 2N fundamental flavours. | contribution 0.60 | 0.19 | 0.04 | asserted 0.99 |
| s2 | The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. | method 0.95 | 0.39 | 0.05 | asserted 1.00 |
| s3 | The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation. | method 0.79 | 0.86 | 0.16 | asserted 1.00 |
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The paper
Original abstract
We study the effective gravitational couplings of four-dimensional Kaluza-Klein compactified gauge theories with eight supercharges. The class of theories we consider are the pure SU(N) Yang-Mills theories at admissible Chern-Simons levels and the conformal gauge theories with 2N fundamental flavours. The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 45 sentences without a confident label
Builds on 4 papers
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In studying the case of non-zero Chern-Simons levels and the case of higher-rank gauge groups, we have extended earlier work [ref] on the study of these effective gravitational couplings.
Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories · Summary and Discussion · 1.00
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In studying the case of non-zero Chern-Simons levels and the case of higher-rank gauge groups, we have extended earlier work [ref] on the study of these effective gravitational couplings.
The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories · Summary and Discussion · 1.00
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This is essentially the five-dimensional uplift of the analysis that was done for the four-dimensional $N=2$ gauge theory with $N_f=2N$ fundamental flavours in [ref] .
Non-perturbative gauge/gravity correspondence in N=2 theories · The Resolvent and the Proposal Revisited · 0.96
Uses the method or tool of 6 papers
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First, we use equivariant localisation to compute $1$-point functions of gauge-invariant chiral observables, as in [ref] .
Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves · Introduction · 1.00
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First, we use equivariant localisation to compute $1$-point functions of gauge-invariant chiral observables, as in [ref] .
Non-perturbative gauge/gravity correspondence in N=2 theories · Introduction · 1.00
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First, we use equivariant localisation to compute $1$-point functions of gauge-invariant chiral observables, as in [ref] .
Chiral observables and S-duality in N = 2* U(N) gauge theories · Introduction · 1.00
Uses data or values from 1 paper
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Up to $1$-instanton, the chiral correlators $V_ℓ$ are given by [ref] : [equation]
Surface operators in 5d gauge theories and duality relations · Expectation Value of Chiral Operators in the Pure Gauge Theory · 0.87
Compares with 4 papers
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[equation] As we have mentioned, on comparing these results — obtained from the Seiberg-Witten geometry — with a localisation computation of the same, one finds a non-dynamical (i.e. independent of Coulomb vevs), purely $q$-dependent mismatch that has interesting parallels with the results found for other asymptotically conformal models in the four-dimensional cases studied in [ref] .
Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories · SU(2) · 0.85
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[equation] As we have mentioned, on comparing these results — obtained from the Seiberg-Witten geometry — with a localisation computation of the same, one finds a non-dynamical (i.e. independent of Coulomb vevs), purely $q$-dependent mismatch that has interesting parallels with the results found for other asymptotically conformal models in the four-dimensional cases studied in [ref] .
Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories · SU(2) · 0.85
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[equation] For $κ= ±1$ we have [equation] Comparing with the localisation results we find a perfect match with the perturbative and instanton contributions provided we set [equation] This is our first check of <ref>.[In [ref] the check of the formulae was done for $κ=0$, as an expansion for large $A$.
The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories · SU(2) · 0.80
Cites as background 12 papers
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A widely studied class of theories in this field are the $𝒩 = 2$ supersymmetric gauge theories, whose low-energy effective dynamics is encoded in the famous Seiberg-Witten geometry [ref] .
Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD · Introduction · 1.00
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A widely studied class of theories in this field are the $𝒩 = 2$ supersymmetric gauge theories, whose low-energy effective dynamics is encoded in the famous Seiberg-Witten geometry [ref] .
Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory · Introduction · 1.00
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As is well known [ref] , the poles are in a one-to-one correspondence with Young tableaux, such that the total number of boxes is equal to $k$, the instanton number.
Instanton counting on blowup. I. 4-dimensional pure gauge theory · The Instanton Partition Function · 0.86
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