Bulk reconstruction in moduli space holography

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,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. t.w.grimm@uu.nl j.monnee@uu.nl d.t.e.vandeheisteeg@uu.nl 1 ar X iv :2 10 3. 12 74 6v 1 [ he pth ] 2 3 M ar 2 02 1