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Four-dimensional Yang-Mills theory with a three-dimensional fermion membrane

We study the four-dimensional Yang-Mills theory in the presence of a three-dimensional membrane of fermions by lattice Monte Carlo simulations. We analyze the phase structure of this theory at finite temperature. Below the phase transition temperature of the pure Yang-Mills theory, we obtain an unconventional phase with spatially-nonuniform vacuum. In this phase, the expectation value of the Polyakov loop is finite on the membrane, and it exponentially decays to zero outside the membrane.