  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.
