The Coulomb potential in gauge theory with a dilaton

TL;DR

This paper explores how the presence and boundary conditions of a dilaton field influence the Coulomb potential in gauge theories, revealing different potential behaviors and constraints on charge isolation.

Contribution

It provides explicit calculations of the Coulomb potential under various dilaton boundary conditions and introduces a new constraint affecting charge confinement.

Findings

Potential behaves as (r + r_φ)^{-1} with vanishing dilaton at infinity.

A gauge coupling-independent dilaton leads to a linear potential.

Isolated SU(N_c) charge cannot be created under the new dilaton constraint.

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