  In a series of recent papers, a special kind of AdS$_2$/CFT$_1$ duality was
observed: the boundary correlators of elementary fields that appear in the
Lagrangian of a 2d conformal theory in rigid AdS$_2$ background are the same as
the correlators of the corresponding primary operators in the chiral half of
that 2d CFT in flat space restricted to the real line. The examples considered
were: (i) the Liouville theory where the operator dual to the Liouville scalar
in AdS$_2$ is the stress tensor; (ii) the abelian Toda theory where the
operators dual to the Toda scalars are the $\mathcal W$-algebra generators;
(iii) the non-abelian Toda theory where the Liouville field is dual to the
stress tensor while the extra gauged WZW theory scalars are dual to non-abelian
parafermionic operators. By direct Witten diagram computations in AdS$_2$ one
can check that the structure of the boundary correlators is indeed consistent
with the Virasoro (or higher) symmetry. Here we consider a supersymmetric
generalization: the $\mathcal N=1$ superconformal Liouville theory in AdS$_2$.
We start with the super Liouville theory coupled to 2d supergravity and show
that a consistent restriction to rigid AdS$_2$ background requires a non-zero
value of the supergravity auxiliary field and thus a modification of the
Liouville potential from its familiar flat-space form. We show that the
Liouville scalar and its fermionic partner are dual to the chiral half of the
stress tensor and the supercurrent of the super Liouville theory on the plane.
We perform tests supporting the duality by explicitly computing AdS$_2$ Witten
diagrams with bosonic and fermionic loops.
