Anomaly cancelling terms from the elliptic genus |
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| Affiliation: | 1. Institute of Mathematics, University of Aberdeen, AB24 3UE, Aberdeen, UK;2. Department of Mathematics, NWF-I Mathematik, Universität Regensburg 93040 Regensburg, Germany;3. Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel;1. Skolkovo Institute of Science and Technology, Moscow, 121205, Russia;2. Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, 127051, Russia;3. Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia;1. Université Paul Sabatier, Institut de Mathématiques de Toulouse, 118 route de Narbonne, F-31062 Toulouse, France;2. Westminster College, 1840 South 1300 East, Salt Lake City, UT 84105, USA;1. Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged, Hungary;2. Department of Theoretical Physics, WIGNER RCP, RMKI, H-1525 Budapest, P.O.B. 49, Hungary |
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| Abstract: | We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external Bμν 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 TrF2 − TrR2 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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