Matching the D64 interaction at two-loops

  • Eric D’Hoker
  • Michael B. Green
  • Boris Pioline
  • Rodolfo Russo
Open Access
Regular Article - Theoretical Physics


The coefficient of the D64 interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop D64 interaction predicted on the basis of S-duality and super-symmetry. A review of the current understanding of the D2p4 interactions in type II superstring theory compactified on a torus Td with p ≤ 3 and d ≤ 4 is included.


Supersymmetry and Duality String Duality 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Eric D’Hoker
    • 1
    • 2
  • Michael B. Green
    • 3
  • Boris Pioline
    • 4
    • 5
  • Rodolfo Russo
    • 6
  1. 1.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesU.S.A.
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.Department of Applied Mathematics and Theoretical PhysicsCambridgeU.K.
  4. 4.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis cedex 05France
  5. 5.Theory Division, CERNGeneva 23Switzerland
  6. 6.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

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