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High Energy Physics - Theory, hep-th
Abstract:
We study certain four-graviton amplitudes in exceptional field theory in
dimensions $D\geq 4$ up to two loops. As the formulation is manifestly
invariant under the U-duality group $E_{11-D}(\mathbb{Z})$, our resulting
expressions can be expressed in terms of automorphic forms. In the low energy
expansion, we find terms in the M-theory effective action of type $R^4$,
$\nabla^4R^4$ and $\nabla^6 R^4$ with automorphic coefficient functions in
agreement with independent derivations from string theory. This provides in
particular an explicit integral formula for the exact string theory $\nabla^6
R^4$ threshold function. We exhibit moreover that the usual supergravity
logarithmic divergences cancel out in the full exceptional field theory
amplitude, within an appropriately defined dimensional regularisation scheme.
We also comment on terms of higher derivative order and the role of the section
constraint for possible counterterms.
