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

TL;DR

This paper finds exact solutions in massless scalar theories across various dimensions, linking their moduli space geometries to Euclidean AdS spaces and revealing connections to instanton densities and de Sitter backgrounds.

Contribution

It provides explicit solutions and explores their geometric and physical properties, connecting scalar theories, instantons, and de Sitter space in a novel way.

Findings

Solutions in D=6,4,3 scalar theories with shared properties.

Moduli space geometries match Euclidean AdS spaces.

Scalar theories relate to de Sitter backgrounds and instanton densities.

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.