The Coulomb potential in gauge theory with a dilaton

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I calculate the potential of a pointlike particle carrying SU(Nc) charge in a gauge theory with a dilaton. The solution depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is of the form (r+rϕ)⁻¹, with rϕ inverse proportional to the decay constant of the dilaton. Another natural constraint for the dilaton ϕ is independence of 1/g²(ϕfϕ) from the gauge coupling g. This requirement yields a potential proportional to r and makes it impossible to create an isolated SU(Nc) charge.