On the integrable gravity coupled to fermions
Abstract
In the present letter we indicate an extension of the pure gravity inverse scattering integration technique to the case when fermions (introduced on the base of supersymmetry) are present. In this way the integrability technique for simple () supergravity in two space-time dimensions coupled to the matter fields taking values in the Lie algebra of group is developed. This theory contains matter living only in one Weyl representation of and represents the reduction to two dimensions of the three-dimensional simple supergravity constructed in [1]. Our spectral linear problem use superspace and covers the complete set of principal bosonic and fermionic equations of motion. This linear system, as in pure gravity, contains only the first order poles with respect to the spectral parameter. The procedure of constructing the exact super-solitonic solutions is outlined.
Cite
@article{arxiv.1611.02924,
title = {On the integrable gravity coupled to fermions},
author = {Vladimir A. Belinski},
journal= {arXiv preprint arXiv:1611.02924},
year = {2017}
}
Comments
Version 1611.02924v1 was withdrawn due to groundless assumption on the existence of the relation (43). In footnote 7 it was stressed that its proof remains to be seen. Analysis showed that such relation indeed is doubtful. Then the extension of the pure gravity inverse scattering method to superspace surely can cover only the simple integrable supergravity with E8(8) symmetry