Two-dimensional gravity from vanishing metrical dimensions

TL;DR

This paper introduces a novel formulation of two-dimensional gravity derived from higher-dimensional theories with a vanishing proper length dimension, allowing for arbitrary curvature solutions unlike traditional constant curvature models.

Contribution

It presents a new dynamical framework for 2D gravity from higher dimensions with a vanishing length dimension, distinct from Kaluza-Klein or Mann-Ross reductions, and shows higher Lovelock terms do not alter the effective equations.

Findings

Solutions with arbitrary curvature are possible.

Higher Lovelock terms do not affect the effective field equations.

Explicit static and homogeneous solutions are provided.

Abstract

We obtain a dynamical formulation of two-dimensional gravity from a non-Einsteinian phase in higher dimensions $(D=3+2n)$. The formalism is associated with (at least) one extra dimension of vanishing proper length, thus being inequivalent to either a Kaluza-Klein compactification or the Mann-Ross dimensional reduction defined upon a singular limit. The emergent solutions admit any arbitrary curvature in contrast with Jackiw-Teitelboim constant curvature gravity. We present the static and homogeneous solutions as explicit examples. The effective field equations are shown to remain unaffected by the inclusion of higher Lovelock terms beyond Einstein.