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Bulk Reconstruction in Moduli Space Holography
High Energy Physics - Theory · Submitted 23 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.
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The abstract, sentence by sentence
It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of $ Sl(2,\mathbb{R})$ boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the $Sl(2)$-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. | background 1.00 | 0.04 | 0.05 | hedged possibility 0.91 |
| s1 | The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. | background 0.90 | 0.08 | 0.03 | asserted 1.00 |
| s2 | We study this sigma-model without any reference to a potentially underlying geometric description. | method 0.57 | 0.87 | 0.03 | asserted 0.94 |
| s3 | Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. | method 0.80 | 0.95 | 0.08 | asserted 0.99 |
| s4 | Specifying a set of $ Sl(2,\mathbb{R})$ boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. | result 0.92 | 0.94 | 0.29 | asserted 1.00 |
| s5 | The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the $Sl(2)$-orbit theorem. | method 0.98 | 0.42 | 0.06 | asserted 1.00 |
| s6 | We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration. | result 0.92 | 0.95 | 0.43 | asserted 1.00 |
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The paper
Original abstract
It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of $ Sl(2,\mathbb{R})$ boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the $Sl(2)$-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.
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References
How the literature uses it
21 arXiv papers cite this in 48 sentences
Papers citing it · 35 sentences without a confident label
Uses its method or tool 1 paper
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The derivation of these formulae utilizes a multi-variable generalization of the CKS recursion [ref] , see also [ref] .
Finiteness Theorems and Counting Conjectures for the Flux Landscape · Introduction · 0.81
Compares with it 2 papers
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Our viewpoint takes a complementary, perhaps more geometric angle compared to the primarily Hodge theoretic approach [ref] to infinite distance limits in the complex structure moduli space of Calabi-Yau threefolds and fourfolds.
Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models · Introduction · 0.83
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Apart from the imaginary prefactor, this agrees precisely with the actions put forward in [ref] and [ref] .
Deformed WZW Models and Hodge Theory -- Part I · Integrability and the On-Shell Action · 1.00
Cites it as background 9 papers
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The raison d'etre of this section is to provide the reader with the main results and applications of Asymptotic Hodge Theory to string compactifications and the Swampland Program [ref] .
A Gravitino Distance Conjecture · Rudiments of Asymptotic Hodge Theory · 1.00
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We keep the discussion brief, and refer the reader to [ref] for more detailed explanations in the mathematical part and to [ref] for the physical interpretation.
End of The World brane networks for infinite distance limits in CY moduli space · Generalities on Calabi Yau Moduli Space and Flux potentials · 1.00
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Specifically, in Sections [ref] and [ref], we will discuss the geometry and the physics at infinite distance in the Kähler and the complex structure moduli of F-theory, respectively, in $4$ and $8$ dimensions, i.e., with $n=3$ and $n=1$ in [ref]; the reported results can thus be viewed as providing intuitions on most general asymptotic regimes of F-theory moduli space.[For recent progress towards the physics of infinite distance limits in various perturbative string setups, see e.g. [ref] and [ref] , which, respectively, analyze the Kähler and the complex structure limits.
On Towers of Light States at Infinite Distance · Introduction · 0.80
What it cites · 78 sentences without a confident label
Builds on 1 paper
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We will mostly take the latter perspective in this work, extend the ideas of [ref] , and show that they are applicable in concrete examples.
Moduli Space Holography and the Finiteness of Flux Vacua · Introduction · 1.00
Uses the method or tool of 1 paper
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We follow the computation in [ref] .
Moduli Space Holography and the Finiteness of Flux Vacua · Imposing the $Q$-constraint on the CKS input data · 1.00
Compares with 1 paper
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In order to simplify our expressions, we have used a basis transformation and a rescaling of the period vector compared to e.g. [ref] .[To be precise, these redefinitions get rid of the intersection number $_111$ appearing with $t^2$ and $t^3$, and the integrated second Chern class in the third entry.
Infinite Distance Networks in Field Space and Charge Orbits · Type $IV_1$ boundaries · 0.96
Cites as support 1 paper
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Furthermore, the fact that the the solutions can be reconstructed starting from the boundary supports the holographic perspective put forward in [ref] and gives an interesting realization of a bulk-boundary correspondence.
Moduli Space Holography and the Finiteness of Flux Vacua · Conclusions · 0.99
Cites as background 12 papers
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Two proposals of coupling of the matter action [ref] to a gravity theory have been studied in [ref] and [ref] .
Moduli Space Holography and the Finiteness of Flux Vacua · Near-boundary solutions at the center of the Poincaré disc · 0.85
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Two proposals of coupling of the matter action [ref] to a gravity theory have been studied in [ref] and [ref] .
Moduli spaces of Calabi-Yau $d$-folds as gravitational-chiral instantons · Near-boundary solutions at the center of the Poincaré disc · 0.85
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This lead to a prominent set of swampland conjectures and emergence proposals [ref] that describe the behaviour and validity of the effective theories when moving to an asymptotic boundary after traversing an infinite geodesic distance.
Emergence and the Swampland Conjectures · Introduction · 0.85
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