  The Schwinger-boson theory of the frustrated square lattice antiferromagnet
yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with
time-reversal symmetry, incommensurate spin correlations and long-range
Ising-nematic order. We obtain an equivalent description of this state using
fermionic spinons (the fermionic spinons can be considered to be bound states
of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin
liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets
of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$
topological and Ising-nematic orders. We describe a Higgs transition out of
this deconfined metallic state into a confining superconducting state which is
usually of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation
of the superconducting order.
