Abstract
Abstract We calculate the heterotic string one-loop diagram in 2 n + 2 dimensions with one external B μν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies Tr F 2 − Tr R 2 in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of “unphysical” modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations.
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