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The String Geometry Behind Topological Amplitudes
High Energy Physics - Theory · Submitted 8 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background.
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The abstract, sentence by sentence
It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $\varOmega$-background of Nekrasov, in the case of opposite deformation parameters $\epsilon_1=-\epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $\mathscr{N}=2$ and $\mathscr{N}=2^*$ theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. | result 0.98 | 0.88 | 0.85 | asserted 1.00 |
| s1 | This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $\varOmega$-background of Nekrasov, in the case of opposite deformation parameters $\epsilon_1=-\epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. | interpretation 0.83 | 0.55 | 0.19 | asserted 1.00 |
| s2 | The analysis is performed on both heterotic and type I strings and for the cases of ordinary $\mathscr{N}=2$ and $\mathscr{N}=2^*$ theories. | method 0.57 | 0.85 | 0.04 | asserted 0.98 |
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The paper
Original abstract
It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $\varOmega$-background of Nekrasov, in the case of opposite deformation parameters $\epsilon_1=-\epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $\mathscr{N}=2$ and $\mathscr{N}=2^*$ theories.
Human review
How the literature uses it
2 arXiv papers cite this in 11 sentences
Papers citing it · 6 sentences without a confident label
Builds on it 1 paper
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By generalising the results of [ref] to include also the second equivariant parameter $ϵ_+$, we obtained an exact realisation of the $Ω$-background in string theory as a 10d Melvin space, where two independent rotations in the Euclidean 4d spacetime are now accompanied by an appropriate supersymmetry-preserving rotation inside K3, together with a shift along a one-cycle of $T^2$.
Refined Topological Amplitudes from the $\Omega$-Background in String Theory · Conclusions · 0.98
Uses its method or tool 1 paper
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Following [ref] , we describe the latter as a Melvin background [ref] , whereby the Euclidean space-time, with complex coordinates $(z^1, z^2)$, is fibered over the $T^2$ via the introduction of the non-trivial monodromy [equation] where $i=1,2$, $x$ is the complex coordinate on the $T^2$ and $m̃_1 , m̃_2 ∈ℤ$ identify a generic one-cycle $m̃_1 + U m̃_2$ in $T^2$.
Refined Topological Amplitudes from the $\Omega$-Background in String Theory · $𝒩=2$ Heterotic String on the $Ω$-Background · 0.98
Compares with it 1 paper
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Notice that these differ from those used by some of the authors in other works, for instance [ref] .] $(a,b)$, while $h$ labels the $ℤ_2$ (un)twisted sectors, and the sum over $g$ implements the orbifold projection.
Refined Topological Amplitudes from the $\Omega$-Background in String Theory · $𝒩=2$ Heterotic String on the $Ω$-Background · 0.83
Cites it as background 2 papers
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An interesting open problem is to unveil the string geometry behind topological amplitudes [ref] .
Refined Topological Amplitudes from the $\Omega$-Background in String Theory · Introduction · 0.92
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See also [ref] for a physical interpretation of the refinement parameters from a world-sheet perspective in string theory.]) topological vertex formalism [ref] .
Little String Instanton Partition Functions and Scalar Propagators · Introduction · 0.90
What it cites · 8 sentences without a confident label
Builds on 4 papers
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This result agrees with and extends to a full string setup previous studies [ref] , where the classical low-energy dynamics of D-branes on Melvin spaces was shown to reproduce the equivariant action of [ref] .
String theory of the Omega deformation · Introduction · 0.90
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This result agrees with and extends to a full string setup previous studies [ref] , where the classical low-energy dynamics of D-branes on Melvin spaces was shown to reproduce the equivariant action of [ref] .
The Omega Deformation From String and M-Theory · Introduction · 0.90
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This result agrees with and extends to a full string setup previous studies [ref] , where the classical low-energy dynamics of D-branes on Melvin spaces was shown to reproduce the equivariant action of [ref] .
Deformed supersymmetric gauge theories from the fluxtrap background · Introduction · 0.90
Compares with 1 paper
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We can finally move to describe systems of D-branes on the anti-self-dual Melvin background with reduced supersymmetry, so that we can compare with the topological amplitudes for open strings [ref] .
Worldsheet Realization of the Refined Topological String · Open Strings on $Melvin×T^2 ×K3$ · 0.81
Cites as background 4 papers
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A possible relation between the $$ background and the NS fluxbrane solution — which is nothing but a synonymous for the Melvin solution — has been already discussed in [ref] .
String theory of the Omega deformation · Comments on Melvin and $$ backgrounds · 0.81
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A possible relation between the $$ background and the NS fluxbrane solution — which is nothing but a synonymous for the Melvin solution — has been already discussed in [ref] .
The Omega Deformation From String and M-Theory · Comments on Melvin and $$ backgrounds · 0.81
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A possible relation between the $$ background and the NS fluxbrane solution — which is nothing but a synonymous for the Melvin solution — has been already discussed in [ref] .
Deformed supersymmetric gauge theories from the fluxtrap background · Comments on Melvin and $$ backgrounds · 0.81
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