The electrostatic interactions between charges in an aqueous solution play an important role in chemistry, biology and material science. The Poisson-Boltzmann(PB) theory gives a simple and powerful description for such systems, taking into account only the Coulombic forces on the mean-field level. Despite its limitations, the PB theory succeeds in capturing most of the underlying physics at high temperatures, low ion valency and weak surface charges. 

One of the limitations of the traditional PB theory is that it fails to give rise to a decrement in the dielectric constant of an ionic solution. The experimentally evident decrement changes the electrostatic interactions in the solution, and can lead to ionic-specific effects. The change in the dielectric constant originates from correlations between ions and the water dipoles, which are not taken into account in the mean-field level theory. We study this effect by going beyond the PB theory, breaking the continuous water dielectric medium into a microscopic model of dipoles and taking into account fluctuations and correlations.  By using a field-theory approach, we are able to obtain a closed analytical formula for the dielectric constant via a one-loop expansion. The predicted dielectric decrement fits well the experimental data through a wide range of inoic concentrations.