  We consider magic-angle graphene in the doping regime around charge
neutrality and study the connection between a recently proposed inter-valley
coherent insulator at zero doping and the neighboring superconducting domes.
The magic-angle graphene continuum model has an emergent U(1) valley-charge
conservation symmetry, and an emergent SU(2) symmetry corresponding to opposite
spin rotations in the two valleys. The inter-valley coherent insulator
spontaneously breaks both these emergent symmetries, and as a result has four
Goldstone modes which couple to doped charge carriers. We derive the effective
interaction mediated by the Goldstone modes, and study its role in electron
pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction,
which is attractive in spin-triplet pairing channels and repulsive in
spin-singlet channels. From a weak-coupling BCS calculation, we find the
leading superconducting instability in the p-wave channel.
