Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality

Abstract

The equations of motion of a super non-Abelian T-dual sigma model on the Lie supergroup $(C^1_1+A)$ in the curved background are explicitly solved by the super Poisson-Lie T-duality. To find the solution of the flat model we use the transformation of supercoordinates, transforming the metric into a constant one, which is shown to be a supercanonical transformation. Then, using the super Poisson-Lie T-duality transformations and the dual decomposition of elements of Drinfel'd superdouble, the solution of the equations of motion for the dual sigma model is obtained. The general form of the dilaton fields satisfying the vanishing $\beta-$function equations of the sigma models is found. In this respect, conformal invariance of the sigma models built on the Drinfel'd superdouble $((C^1_1+A),I_{(2|2)})$ is guaranteed up to one-loop, at least.