D6ℛ4 amplitudes in various dimensions
- 228 Downloads
Four-graviton couplings in the low energy effective action of type II string vacua compactified on tori are strongly constrained by supersymmetry and U-duality. While the ℛ4 and D4ℛ4 couplings are known exactly in terms of Langlands-Eisenstein series of the U-duality group, the D6ℛ4 couplings are not nearly as well understood. Exploiting the coincidence of the U-duality group in D = 6 with the T-duality group in D = 5, we propose an exact formula for the D6ℛ4 couplings in type II string theory compactified on T4, in terms of a genus-two modular integral plus a suitable Eisenstein series. The same modular integral computes the two-loop correction to D6ℛ4 in 5 dimensions, but here provides the non-perturbative completion of the known perturbative terms in D = 6. This proposal hinges on a systematic re-analysis of the weak coupling and large radius of the D6ℛ4 in all dimensions D ≥ 3, which fills in some gaps and resolves some inconsistencies in earlier studies.
KeywordsSuperstrings and Heterotic Strings Nonperturbative Effects String Duality Effective field theories
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- G. Bossard and A. Kleinschmidt, to appear.Google Scholar
- N. Kawazumi, Johnson’s homomorphisms and the Arakelov-Green function, arXiv:0801.4218.
- B. Pioline and R. Russo, to appear.Google Scholar
- M.A.A. van Leeuwen, A.M. Cohen and B. Lisser, LiE, a package for Lie group computations, http://wwwmathlabo.univ-poitiers.fr/∼maavl/LiE/.