  We study the Kaluza-Klein spectrum of warped $AdS_3$ compactifications of
type IIB with five-form flux which are dual to $\mathcal{N}=(0,2)$ SCFTs in two
dimensions. We prove that the spectra of fluctuations of both the spin 2 sector
of the graviton and the axio-dilaton are bounded. At the bound the modes have
the correct quantum numbers to be chiral primaries and descendants thereof
respectively. Moreover, we prove that the same modes give rise to superpartners
in the dilatino spectrum. Our results show that a subset of the mesonic chiral
ring of the dual SCFT is isomorphic to the first Kohn-Rossi cohomology groups.
As an example, we consider the compactification of four-dimensional $Y^{p,q}$
theories on Riemann surfaces for the case of the universal twist. We conclude
by studying fluctuations of the three-form, where we are able to identify Betti
multiplets after imposing some mild assumptions.
