Bulk Reconstruction in Moduli Space Holography

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.

arXiv comment44 pages plus appendices, 1 figure

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Cited by in corpus (12)

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• Moduli Space Holography and the Finiteness of Flux Vacua
• Moduli Stabilization in Asymptotic Flux Compactifications
• Physics of Infinite Complex Structure Limits in eight Dimensions
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• Deformed WZW Models and Hodge Theory -- Part I
• The Algebraic Structure Underlying Pole-Skipping Points
• The Tadpole Conjecture in Asymptotic Limits