  We find a phenomenon in a non-gravitational gauge theory analogous to the
replica wormhole in a quantum gravity theory. We consider a reservoir of a
scalar field coupled with a gauge theory contained in a region with a boundary
by an axion-like coupling. When the replica trick is used to compute the
entanglement entropy for a subregion in the reservoir, a tuple of instantons
distributed across the replica sheets gives a non-perturbative contribution. As
an explicit and solvable example, we consider a discrete scalar field coupled
to a 2d pure gauge theory and observe how the replica instantons reproduce the
entropy directly calculated from the reduced density matrix. In addition, we
notice that the entanglement entropy can detect the confinement of a 2d gauge
theory.
