Matching the D 6ℛ4 interaction at two-loops

Eric D’hoker (1) , Michael B. Green (2) , Boris Pioline (3, 4, 5) , Rodolfo Russo (6)

1 UCLA - University of California [Los Angeles]
2 DAMTP - Department of Applied Mathematics and Theoretical Physics
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
4 SU - Sorbonne Université
5 UPMC - Université Pierre et Marie Curie - Paris 6
6 School of Physics and Astronomy [London]

The coefficient of the $D^6 {\cal R}^4$ 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 $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Eric D’hoker, Michael B. Green, Boris Pioline, Rodolfo Russo. Matching the D 6ℛ4 interaction at two-loops. Journal of High Energy Physics, 2015, 2015 (1), pp.31. ⟨10.1007/JHEP01(2015)031⟩. ⟨hal-01101710⟩