nLab D=2 gravity

Idea

One may consider gravity (general relativity, Einstein's equations) on spacetimes of dimension 2.

Examples

Relativistic string worldsheets

If 2d gravity is coupled to scalar “matter”-fields with values in some target space, then this may be regarded as the worldsheet-sigma-model quantum field theory of a relativistic string propagating on that target spacetime.

2d Dilaton gravity – JT gravity

A form of 2d dilaton gravity is known as Jackiw-Teitelboim gravity, or JT-gravity, for short.

JT-gravity gives a good approximation to the AdS-factor in the near horizon geometry $AdS_2\times S^{d-2}$ of near-extremal black holes in $d$-dimensional spacetime (NSST18, MTV18).

Related concepts

• Wheeler superspace

• supersymmetric quantum mechanics

• relativistic stringsigma-model

• Jackiw-Teitelboim gravity

• Liouville theory

References

• Paul Ginsparg, Gregory Moore: Lectures on 2D gravity and 2D string theory (TASI 1992) [arXiv:hep-th/9304011]

• J. Ambjørn, T. Budd: Two-Dimensional Quantum Geometry, Acta Physica Polonica B 44 12 (2013) 2537 [arXiv:1310.8552, doi:10.5506/APhysPolB.44.2537]