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Two-dimensional gravity and nonlinear gauge theory. (English) Zbl 0807.53070

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.

MSC:

53Z05 Applications of differential geometry to physics
81T13 Yang-Mills and other gauge theories in quantum field theory