Ikeda, Noriaki Two-dimensional gravity and nonlinear gauge theory. (English) Zbl 0807.53070 Ann. Phys. 235, No. 2, 435-464 (1994). Summary: We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincaré algebra, which is the new Yang-Mills-like formulation of the gravitational theory. As typical examples, we investigate \(\mathbb{R}^ 2\) gravity with dynamical torsion and generic form of “dilation” gravity. The supersymmetric extension of this theory is also discussed. Cited in 1 ReviewCited in 107 Documents MSC: 53Z05 Applications of differential geometry to physics 81T13 Yang-Mills and other gauge theories in quantum field theory Keywords:gauge theory; nonlinear Lie algebras; two-dimensional gravity; nonlinear Poincaré algebra; supersymmetric extension × Cite Format Result Cite Review PDF Full Text: DOI arXiv