  We compute the off-shell spectrum of supergravity on AdS$_2\times S^2$ by
explicit diagonalization of the equations of motion for an effective AdS$_2$
theory where all fields are dualized to scalars and spin-${1\over 2}$ fermions.
Classifying all bulk modes as physical, gauge violating, and pure gauge let us
identify boundary modes as physical fields on $S^2$ that are formally pure
gauge but with gauge function that is non-normalizable on AdS$_2$. As an
application we compute the leading quantum correction to AdS$_2\times S^2$ as a
sum over physical fields including boundary states.
