D64 amplitudes in various dimensions

Open Access
Regular Article - Theoretical Physics

Abstract

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.

Keywords

Superstrings and Heterotic Strings Nonperturbative Effects String Duality Effective field theories 

Notes

Open Access

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.

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Copyright information

© 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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