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

Abstract

Three exact solutions say ${\varphi }_0$ of massless scalar theories on Euclidean space, i.e. $D=6{\varphi }^3$, $D=4{\varphi }^4$ and $D=3{\varphi }^6$ 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 ${\varphi }_0$ can be described as a stable tachyon. In D=4 we recognize that the SU(2) instanton density is proportional to ${\varphi }_0^4$. The original action $S[\varphi ]$ written in terms of new scalars $\tilde{\varphi }=\varphi -{\varphi }_0$ is shown to be equivalent to an interacting scalar theory on $D$-dimensional de Sitter background.

The title is changed! Eq.(19) and Appendix A are added. To appear in PRD

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Cited by in corpus (4)

• Fubini vacua as a classical de Sitter vacua
• Dual Instantons in Anti-membranes Theory
• Non-Minimally Coupled Pseudoscalars in AdS_4 for Instantons in CFT_3
• ${\varphi }^4$ model on a circle