We study the ground-state of a gas of N Bosons in ${\mathbb R}^3$ interacting via three-body interactions in the Gross-Pitaevskii regime. In this regime the interaction potential scales as $N V(N^{1/2}(x-y,x-z))$ and is so singular that the mean-field approximation fails to describe the system at main order. We will see that the three-body correlation structure creates a shift in energy of order $N$ and we will explain how to describe it. The effective theory is then given by the 3D energy-critical non-linear Schrödinger functional. This is joint work with P.T. Nam and J. Ricaud.

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