Nonabelian T-duals of the flat background

Abstract

Classification of nonabelian T-duals of the flat matric in D=4 with respect to the four-dimensional continuous subgroups of the Poincare group is given. After dualizing the flat background we identify majority of dual models as conformal sigma models in plane- parallel wave backgrounds, most of them having torsion. We give their form in Brinkmann coordinates. Besides the pp-waves we find several diagonalizable curved metrics with nontrivial scalar curvature and torsion.Due to the nonabelian T-duality, we find general solution of classical field equations of all the sigma models in terms of d'Alembert solutions of wave equation.