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# Advances in Theoretical and Mathematical Physics

## Volume 19 (2015)

### Number 6

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

Pages: 1249 – 1275

DOI: http://dx.doi.org/10.4310/ATMP.2015.v19.n6.a3

#### Author

#### Abstract

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.