Ramifications of Lineland
Daniel Grumiller, Rene Meyer
TL;DR
This survey analyzes gravity in two dimensions through the lens of dilaton gravity, presenting a nonlinear gauge-theory reformulation that yields complete classical solutions labeled by a mass parameter and governed by invariants I(X) and w(X). It connects this formalism to 2D string theories, especially 0A/0B backgrounds, and to exact string black holes, clarifying how target-space actions arise and how limits recover familiar models like the Witten BH and JT gravity. The work also explores topological and non-topological extensions, including Maxwell and matter fields, and discusses how integrability is affected by matter content. In particular, the exact string black hole (ESBH) background is highlighted for its non-perturbative, globally valid action and its interpolation between well-known 2D gravity backgrounds, with a dual ESNS solution illuminating the landscape of 2D string geometries.
Abstract
A non-technical overview on gravity in two dimensions is provided. Applications discussed in this work comprise 2D type 0A/0B string theory, Black Hole evaporation/thermodynamics, toy models for quantum gravity, for numerical General Relativity in the context of critical collapse and for solid state analogues of Black Holes. Mathematical relations to integrable models, non-linear gauge theories, Poisson-sigma models, KdV surfaces and non-commutative geometry are presented.