  The large-charge master field which generates all n-point correlation
functions with an insertion of large charge Q in non-relativistic conformal
field theory is obtained. This field is used to compute Schr\"odinger-invariant
n-point correlation functions of large-charge operators via a direct evaluation
of the path integral. Conformal dimensions are found to agree with calculations
based on the state-operator correspondence. The master field solution exhibits
an emergent harmonic trap whose frequency is a function of the Euclidean time.
The large-charge effective action with operator insertions describes a droplet
of superfluid matter whose spatial size scales with the time separation of
sources. The solution is used to compute Schr\"odinger symmetry breaking
corrections in the large-charge effective field theory (EFT) due to a finite
scattering length in the fundamental theory of fermions near unitarity. The
scaling of these effects in the large-charge power counting scheme is
established, and the size of the effects is quantified using input from quantum
Monte Carlo simulations of the near-unitary gas, as well as from the large-N
expansion at large charge.
