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F-theory Flux Vacua and Attractor Equations
High Energy Physics - Theory · Submitted 23 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory.
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The abstract, sentence by sentence
We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. | background 0.60 | 0.63 | 0.03 | asserted 0.72 |
| s1 | Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. | method 0.73 | 0.95 | 0.05 | asserted 0.95 |
| s2 | It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. | result 1.00 | 0.91 | 0.20 | asserted 1.00 |
| s3 | We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. | interpretation 1.00 | 0.56 | 0.56 | hedged possibility 0.60 |
| s4 | In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously. | result 1.00 | 0.94 | 0.46 | asserted 1.00 |
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The paper
Original abstract
We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.
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References
How the literature uses it
5 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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The problem of the stabilisation of those moduli is however beyond the scope of the present paper, and we refer the reader to [ref] and the references therein for works on the subject.
Towards a complete mass spectrum of type-IIB flux vacua at large complex structure · Effective theory · 0.99
What it cites · 19 sentences without a confident label
Uses the method or tool of 1 paper
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While this choice is sufficient for the current purpose, further quantum corrections can be easily calculated by using mirror symmetry technique or supersymmetric localization approach as in [ref] .
Exact Kahler Potential for Calabi-Yau Fourfolds · Setup · 0.96
Uses data or values from 6 papers
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As an explicit example of F-theory compactification, here we consider the background studied in [ref] (see also [ref] ), whose period integrals and topological intersection matrix are given by [equation] [equation] with the Euler characteristic $χ= 1860$.
Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications · Setup · 0.86
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As an explicit example of F-theory compactification, here we consider the background studied in [ref] (see also [ref] ), whose period integrals and topological intersection matrix are given by [equation] [equation] with the Euler characteristic $χ= 1860$.
Computing Brane and Flux Superpotentials in F-theory Compactifications · Setup · 0.86
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As an explicit example of F-theory compactification, here we consider the background studied in [ref] (see also [ref] ), whose period integrals and topological intersection matrix are given by [equation] [equation] with the Euler characteristic $χ= 1860$.
On N=1 4d Effective Couplings for F-theory and Heterotic Vacua · Setup · 0.86
Cites as background 10 papers
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Here we argue that our findings are deeply connected with a seemingly different topic in the 4D supergravity referred to as the attractor mechanism [ref] (see also [ref] ), where the normalized flux superpotential $Z=e^K/2W$ of a system can be identified as a central charge of the underlying algebra which is subject to a monotonic flow along the radial direction of a background.
Erice Lectures on Black Holes and Attractors · Flux Vacua and Attractor Equations · 0.87
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The F-theory compactification also generically admits a superpotential of the form [ref] [equation] in the presence of four-form fluxes $G_4$, which is inherited from a duality between F-theory and M-theory on the same manifold [ref] .
Les Houches Lectures on Constructing String Vacua · Setup · 0.93
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Since the numerical value of $ϵ$ obtained in our analysis is sufficiently small to realize this naive expectation, it would be interesting to cast this idea in a rigorous setup.[For the details about quantum corrections in F-theory, we refer the reader to, for instance, [ref] .]
F-theory Vacua and $\alpha'$-Corrections · Distribution of non-supersymmetric flux vacua · 0.88
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