Potentials of pointlike particles in gauge theory with a dilaton

I examine the potential of a pointlike particle carrying SU (N _c) charge in a gauge theory with a dilaton. The potential depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is a regulatized Coulomb potential of the form (r+r _ϕ)⁻¹, withr _ϕ, inversely proportional to the decay constant of the dilaton. Another natural constraint on the dialaton ϕ is independence of (1/g ²) exp(ϕ/f_ϕ) from the gauge couplingg. This requirement yields a confining potential proportional tor.