  We consider heterotic strings on a warped Eguchi-Hanson space with five-brane
and line bundle gauge fluxes. The heterotic string admits an exact CFT
description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a
specific double scaling limit in which the blow-up radius and the string scale
are sent to zero simultaneously. This allows us to compute the perturbative 6D
spectra for these models in two independent fashions: i) Within the
supergravity approximation we employ a representation dependent index; ii) In
the double scaling limit we determine all marginal vertex operators of the
coset CFT. To achieve agreement between the supergravity and the CFT spectra,
we conjecture that the untwisted and the twisted CFT states correspond to the
same set of hyper multiplets in supergravity. This is in a similar spirit as a
conjectured duality between asymptotically linear dilaton CFTs and little
string theory living on NS-five-branes. As the five-brane charge is
non-vanishing, heterotic (anti-)five-branes have to be added in order to cancel
irreducible gauge anomalies. The local spectra can be combined in such a way
that supersymmetry is preserved on the compact resolved T^4/Z_2 orbifold by
choosing the local gauge fluxes appropriately.
