Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 6

Beltrami–Courant differentials and $G_{\infty}$-algebras

Pages: 1249 – 1275



Anton M. Zeitlin (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.; Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France; and IPME RAS, St. Petersburg, Russia)


Using the symmetry properties of two-dimensional sigma models, we introduce a notion of the Beltrami–Courant differential, so that there is a natural homotopy Gerstenhaber algebra related to it. We conjecture that the generalized Maurer–Cartan equation for the corresponding $L_{\infty}$ subalgebra gives solutions to the Einstein equations.

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