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Supersymmetric Flux Compactifications and Calabi-Yau Modularity
High Energy Physics - Theory · Submitted 16 Jan 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper, we propose that supersymmetric flux vacua are modular.
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The abstract, sentence by sentence
Flux compactification of IIB string theory associates special points in Calabi-Yau moduli space to choices of (pairs of) integral three-form fluxes. In this paper, we propose that supersymmetric flux vacua are modular. That is, to a supersymmetric flux vacuum arising in a variety defined over $\mathbb{Q}$, we associate a two-dimensional Galois representation that we conjecture to be modular. We provide numerical evidence for our conjecture by examining flux vacua arising on the octic hypersurface in $\mathbb{P}^{4}(1,1,2,2,2)$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Flux compactification of IIB string theory associates special points in Calabi-Yau moduli space to choices of (pairs of) integral three-form fluxes. | background 1.00 | 0.07 | 0.03 | asserted 1.00 |
| s1 | In this paper, we propose that supersymmetric flux vacua are modular. | contribution 0.98 | 0.52 | 0.76 | speculative 0.54 |
| s2 | That is, to a supersymmetric flux vacuum arising in a variety defined over $\mathbb{Q}$, we associate a two-dimensional Galois representation that we conjecture to be modular. | contribution 0.89 | 0.42 | 0.54 | speculative 0.98 |
| s3 | We provide numerical evidence for our conjecture by examining flux vacua arising on the octic hypersurface in $\mathbb{P}^{4}(1,1,2,2,2)$. | contribution 0.56 | 0.95 | 0.07 | asserted 0.98 |
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The paper
Original abstract
Flux compactification of IIB string theory associates special points in Calabi-Yau moduli space to choices of (pairs of) integral three-form fluxes. In this paper, we propose that supersymmetric flux vacua are modular. That is, to a supersymmetric flux vacuum arising in a variety defined over $\mathbb{Q}$, we associate a two-dimensional Galois representation that we conjecture to be modular. We provide numerical evidence for our conjecture by examining flux vacua arising on the octic hypersurface in $\mathbb{P}^{4}(1,1,2,2,2)$.
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References
How the literature uses it
29 arXiv papers cite this in 100 sentences
Papers citing it · 67 sentences without a confident label
Builds on it 2 papers
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Section 3 extends the analysis of [ref] to several prominent Calabi-Yau threefolds that have been considered in the literature and for which flux vacua are known to exist, adding also a remark about modular black hole attractors.
Flux vacua and modularity · Introduction · 0.99
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Finally, in Section [ref] we will apply the F-theory framework to the example of [ref] , and derive two one-parameter families of elliptic curves that exactly reproduce the eigenforms associated to two families of rational models for the supersymmetric flux compactifications arising in the octic Calabi-Yau hypersurface in $(1,1,2,2,2)$.
Flux Modularity, F-Theory, and Rational Models · Introduction · 0.93
Compares with it 2 papers
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For the $ϕ$ points studied in [ref] , we have checked that the modular forms associated to the curves in [ref] exactly match those associated to Eq. [ref], and similarly the forms associated to Eq. [ref] match those associated to Eq. [ref].
Flux Modularity, F-Theory, and Rational Models · The Elliptic Curves · 0.82
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This phenomenon does not appear in the examples studied in [ref] , nor is it true for the other manifolds we study.
Flux Vacua and Modularity for $\mathbb{Z}_2$ Symmetric Calabi-Yau Manifolds · Rational points and elliptic modular forms · 0.95
Cites it as support 2 papers
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We will study supersymmetric vacuum configurations, and provide new examples in support of the flux modularity conjecture [ref] .
Investigations in Calabi-Yau modularity and mirror symmetry · Resuming the computation · 0.96
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We therefore find that any solution satisfying the warped compactification ansatz requires [ref] [equation] This condition does not pose an independent constraint on fluxes leading to supersymmetric solutions however, as it follows from [ref], [ref], and reality of the dilaton: [equation] the inequality following from the Hodge-Riemann bilinear identities [ref] for primitive (2,1)-forms.
Time reversal and $\boldsymbol{CP}$ invariance in Calabi-Yau compactifications · Supersymmetric flux vacua and rank 2 attractors · 0.96
Cites it as background 18 papers
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In this case the two-dimensional subspaces with the Hodge type $(2,1)+(1,2)$ correspond to weight-two modular forms, whereas the spaces with Hodge type $(3,0)+(0,3)$ correspond to weight-four modular forms [ref] .
Flux Vacua and Modularity for $\mathbb{Z}_2$ Symmetric Calabi-Yau Manifolds · Calabi-Yau Modularity · 0.86
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A natural question in the context of the flux vacua modularity conjecture is whether its reverse also holds, an issue that was addressed in [ref] .
Flux vacua and modularity · On the reverse of the modularity conjecture · 0.84
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Suppose we want to show the sub-Hodge structure $(H^n,a (X, ℚ),F_0^p,a )$ on the Fermat type CY $n$-fold $ℱ_n$ has a two dimensional direct summand $𝐇^n_a,1$ over a real number field $k$ with Hodge decomposition [equation] This equation is equivalent to the existences of two linearly independent charges $γ_1,γ_2$ in the space $H^n(ℱ_n,ℚ) ⊗_ℚ k$ with Hodge decomposition [equation] Here the terminology `charge' comes from string theory, which means the charges of BPS black holes [ref] .
Rank-2 attractors and Fermat type CY $n$-folds · The charge equations for the Hodge structures to split · 0.84
What it cites · 11 sentences without a confident label
Cites as background 1 paper
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On the other hand, for more general fields it is not known what sort of automorphic object we expect to find; see e.g. [ref] for recent progress on the study of modularity for elliptic curves over more complicated number fields.
Potential automorphy over CM fields · Modularity From Supersymmetric Flux Compactifications · 0.90
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