  We compute a nonperturbative effective potential between two static fermions
in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair
production is suppressed, to make possible an exact analytic solution in the
form of a coherent state of bosons that form clouds around the sources. The
effective potential is essentially an interference term between individual
clouds. The model is regulated with Pauli-Villars bosons and fermions, to
achieve consistent quantization and renormalization of masses and couplings.
This extends earlier work on scalar Yukawa theory where Pauli-Villars
regularization did not play a central role. The key result is that the
nonperturbative solution restores rotational symmetry even though the
light-front formulation of Yukawa theory, with its preferred axis, appears
antithetical to such a symmetry.
