  We study the elliptic genera of the non-critical strings of six dimensional
superconformal field theories from the point of view of the strings' worldsheet
theory. We formulate a general ansatz for these in terms of characters of the
affine Lie algebra associated to the 6d gauge group at negative level, and
provide ample evidence for the validity of this ansatz for 6d theories obtained
via F-theory compactification on elliptically fibered Calabi-Yau manifolds over
a Hirzebruch base. We obtain novel closed form results for many elliptic genera
in terms of our ansatz, and show that our results specialize consistently when
moving along Higgsing trees.
