The Coulomb potential in gauge theory with a dilaton

Abstract

I calculate the potential of a pointlike particle carrying SU$(N_c)$ 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 $(r+r_ϕ)^{-1}$, with $r_ϕ$ inverse proportional to the decay constant of the dilaton. Another natural constraint for the dilaton $ϕ$ is independence of $\frac{1}{g^2}\exp(\fracϕ{f_ϕ})$ from the gauge coupling $g$. This requirement yields a potential proportional to $r$ and makes it impossible to create an isolated SU$(N_c)$ charge.