Non-linear Laplace equation, de Sitter vacua and information geometry

Abstract

Three exact solutions say $\phi_0$ of massless scalar theories on Euclidean space, i.e. $D=6 \phi^3$, $D=4 \phi^4$ and $D=3 \phi^6$ models are obtained which share similar properties. The information geometry of their moduli spaces coincide with the Euclidean ${AdS}_7$, ${AdS}_5$ and ${AdS}_4$ respectively on which $\phi_0$ can be described as a stable tachyon. In D=4 we recognize that the SU(2) instanton density is proportional to $\phi_0^4$. The original action $S[\phi]$ written in terms of new scalars ${\tilde \phi}=\phi-\phi_0$ is shown to be equivalent to an interacting scalar theory on $D$-dimensional de Sitter background.