Vertex Operator Solutions of 2d Dimensionally Reduced Gravity

Denis Bernard, Nicolas Regnault

Commun.Math.Phys. 210 (2000) 177-201, solv-int/9902017

abstract:We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neugebauer symmetry.

subject: integrable systems