Fixing EFT equations with a reservoir model

Abstract

Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The resulting action principle helps to define a well-posed problem introducing a mechanism to control UV behavior. Physically this is achieved by dissipating the energy in the short-wavelength modes into the extra dimension. We examine the resulting dynamics and compare it to alternative proposals for studying such theories in the non-linear regime.

Figures (2)

• Figure 1: The $L_2$ norm of the differences between the $C_{1,2}$ solutions and the original problem at $\gamma=0.2$. A stable evolution is found for all methods. The smallest errors are obtained in the fixed method $C_2$ and with $\alpha \ll \gamma$ for $C_1$.
• Figure 2: The $L_2$ norm of the differences between the $C_{1,2}$ solutions and the original problem at $\gamma=20$. The smallest errors are obtained in the fixed method $C_2$ and with $\alpha \ll \gamma$ for $C_1$. The addition of the damping reduces the differences with respect to the full solution for values of $\alpha\approx \gamma$.