Affine characters at negative level and elliptic genera of non-critical strings

Abstract

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.

arXiv comment45 pages, many tables; v2: typos corrected, new closed form results for the elliptic genera of a B4 and an E7 theory conjectured; v3: version published in JHEP, link to Mathematica readable file containing negative level affine characters underlying computations in paper included

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