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Flux vacua and modularity
High Energy Physics - Theory · Submitted 2 Mar 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactifications for which such vacua are known to exist.
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The abstract, sentence by sentence
Geometric modularity has recently been conjectured to be a characteristic feature for flux vacua with $W=0$. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactifications for which such vacua are known to exist. The analysis of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Geometric modularity has recently been conjectured to be a characteristic feature for flux vacua with $W=0$. | background 1.00 | 0.04 | 0.08 | speculative 0.92 |
| s1 | This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactifications for which such vacua are known to exist. | contribution 0.98 | 0.96 | 0.47 | asserted 0.91 |
| s2 | The analysis of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold. | result 0.97 | 0.87 | 0.18 | asserted 1.00 |
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The paper
Original abstract
Geometric modularity has recently been conjectured to be a characteristic feature for flux vacua with $W=0$. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactifications for which such vacua are known to exist. The analysis of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold.
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References
How the literature uses it
10 arXiv papers cite this in 14 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 9 papers
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Recently there has been much progress, both from the direction of these attractor points away from symmetric loci in moduli space [ref] , as well as for supersymmetric flux vacua [ref] .
Beyond Large Complex Structure: Quantized Periods and Boundary Data for One-Modulus Singularities · Introduction · 0.88
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[ref] — are expected either to be truncated $𝒩=1$ Calabi–Yau orientifold compactifications [ref] or to correspond to $𝒩=2$ gauged supergravity theories [ref] .
On the Geometry of N=2 Minkowski Vacua of Gauged N=2 Supergravity Theories in Four Dimensions · Introduction · 0.82
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Although various references have made progress towards computing the $L$-functions of varieties from string theory (see e.g. [ref] ), to date no clear, string theoretic motivation for the mod-$p$ reductions of a threefold or other variety have ever been given.
Flux Modularity, F-Theory, and Rational Models · Conclusion · 0.90
What it cites · 42 sentences without a confident label
Builds on 1 paper
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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.
Supersymmetric Flux Compactifications and Calabi-Yau Modularity · Introduction · 0.99
Uses the method or tool of 3 papers
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In the present paper, following [ref] , motives are viewed as representations of the Galois group because this approach provides the simplest and most effective approach.
Emergent spacetime from modular motives · Motivic $L$-series in weighted hypersurfaces · 0.81
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The orientifold projection is derived in [ref] via Sen's method [ref] from the CY fourfold $X_4^24 ∈_(1,1,1,1,8,12)[24]$, whose Euler number $χ=23,328$ and cohomology has been computed in ref.
Flux Compactifications on Calabi-Yau Threefolds · The one-parameter octic $X_3^8∈_(1,1,1,1,4)[8]$ · 0.80
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The orientifold projection is derived in [ref] via Sen's method [ref] from the CY fourfold $X_4^24 ∈_(1,1,1,1,8,12)[24]$, whose Euler number $χ=23,328$ and cohomology has been computed in ref.
Orientifold Limit of F-theory Vacua · The one-parameter octic $X_3^8∈_(1,1,1,1,4)[8]$ · 0.80
Compares with 2 papers
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This is independent of the approach in [ref] via the Shioda-Katsura decomposition of the cohomology of curves embedded in weighted hypersurfaces.
Complex Multiplication Symmetry of Black Hole Attractors · A modular rank two attractor on $X_3^6$ · 0.96
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This is independent of the approach in [ref] via the Shioda-Katsura decomposition of the cohomology of curves embedded in weighted hypersurfaces.
Complex Multiplication of Exactly Solvable Calabi-Yau Varieties · A modular rank two attractor on $X_3^6$ · 0.96
Cites as background 35 papers
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The class of smooth Calabi-Yau hypersurfaces in weighted projective space consists of four spaces, all of which were considered first in the context of flux vacua in [ref] .
Enumerating Flux Vacua with Enhanced Symmetries · Flux vacua for one-parameter weighted hypersurfaces · 0.87
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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] .
Supersymmetric Flux Compactifications and Calabi-Yau Modularity · On the reverse of the modularity conjecture · 0.84
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The main interest in the earlier work cited above was to apply this construction to the holomorphic threeform $$, which leads to the concept of the $$-motive [ref] (see also [ref] ), and to relate the resulting modular and automorphic forms to the modular structure on the worldsheet.
The Langlands Program and String Modular K3 Surfaces · Motivic $L$-series in weighted hypersurfaces · 0.80
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