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 $(r+r_{\varphi }{)}^{-1}$, with $r_{\varphi }$ inverse proportional to the decay constant of the dilaton. Another natural constraint for the dilaton $\varphi$ is independence of $\frac{1}{g^2}\exp (\frac{\varphi }{f_{\varphi }})$ 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.

Comments: 7 pages, LaTex, uses amssymb. A note and a reference added