  We obtain a simple obstruction to embedding groups into the analytic
diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which
embed into $\mathrm{Diff}_{+}^{\omega }(\mathbb{S}^1)$. We also prove that a
branch group does not embed into $\mathrm{Diff}_{+}^{\omega }(\mathbb{S}^1)$.
