D64 amplitudes in various dimensions

Open Access
Regular Article - Theoretical Physics


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 D44 couplings are known exactly in terms of Langlands-Eisenstein series of the U-duality group, the D64 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 D64 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 D64 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 D64 in all dimensions D ≥ 3, which fills in some gaps and resolves some inconsistencies in earlier studies.


Superstrings and Heterotic Strings Nonperturbative Effects String Duality Effective field theories 


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© The Author(s) 2015

Authors and Affiliations

  1. 1.CERN PH-TH, Case C01600, CERNGeneva 23Switzerland
  2. 2.Sorbonne Universités, UPMC Université Paris 6, UMR 7589ParisFrance
  3. 3.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis cedex 05France

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