  Since the discovery of the pseudogap and Fermi arc states in underdoped
cuprates, the understanding of such non-Fermi-liquid states and the associated
violation of Luttinger's theorem have been the central theme in correlated
electron systems. However, still lacking is a well-accepted theoretical
framework to unambiguously explain these metallic states that are clearly
beyond Landau's Fermi liquid and Luttinger's theorem of a Fermi surface and
electron filling. Here, we design a lattice model of orthogonal metals with
fermion and Ising matter fields coupled to topological order and, by solving
the model via unbiased quantum Monte Carlo simulation at generic electron
fillings, find that the system gives birth to phenomena of the Fermi arc and
pseudogap in the single-particle spectrum that go beyond the Luttinger sum rule
with broken Fermi surface but no symmetry breaking. The pseudogap and Fermi
arcs coexist with a background of a deconfined Z2 gauge field, and we further
find that the confinement transition of the gauge field triggers a
superconductivity instability and that the hopping of the gauge-neutral
fermions brings the "large" Fermi surface back from the Fermi arc state. Our
unbiased numerical results provide a concrete model realization and theoretical
framework for the coupling between gauge field and fermions and, in the
process, generate the rich phenomena of the pseudogap, the Fermi arc, and
superconductivity in generic correlated electron systems.
