Twisted Self-Duality of Dimensionally Reduced Gravity and Vertex Operators
High Energy Physics - Theory
2008-11-26 v1 General Relativity and Quantum Cosmology
Exactly Solvable and Integrable Systems
solv-int
Abstract
The Geroch group, isomorphic to the SL(2,R) affine Kac-Moody group, is an infinite dimensional solution generating group of Einstein's equations with two surface orthogonal commuting Killing vectors. We introduce another solution generating group for these equations, the dressing group, and discuss its connection with the Geroch group. We show that it acts transitively on a dense subset of moduli space. We use a new Lax pair expressing a twisted self-duality of this system and we study the dressing problem associated to it. We also describe how to use vertex operators to solve the reduced Einstein's equations. In particular this allows to find solutions by purely algebraic computations.
Keywords
Cite
@article{arxiv.hep-th/9712254,
title = {Twisted Self-Duality of Dimensionally Reduced Gravity and Vertex Operators},
author = {D. Bernard and B. Julia},
journal= {arXiv preprint arXiv:hep-th/9712254},
year = {2008}
}
Comments
33 pages, LaTeX, Bonne Ann\'ee