Loops in exceptional field theory

Understand

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.