nLab D=2 quantum gravity

Idea

In the very low number of just 2 dimensions, quantum gravity is comparatively trivial and can be completely understood. While trivial as a theory of quantum gravity on a 2d spacetime, when that spacetime is regarded instead as the worldsheet of a string, then in fact the string’s worldsheet sigma-model theory is a theory of 2d quantum gravity (before the usual gravitational gauge fixing in 2d, which then makes what remains a conformal field theory, instead).

Related concepts

• world sheets for world sheets

• D=3 quantum gravity

References

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

Via matrix models:

• Edouard Brézin, Jean Zinn-Justin: Renormalization Group Approach to Matrix Models, Phys. Lett. B 288 (1992) 54-58 [arXiv:hep-th/9206035, doi:10.1016/0370-2693(92)91953-7]

• Astrid Eichhorn, Tim Koslowski: Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group, Phys. Rev. D 88 (2013) 084016 [arXiv:1309.1690, doi:10.1103/PhysRevD.88.084016]