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.
Highlights
A review of the super Poisson-Lie symmetric sigma models on Lie supergroupsLet us briefly review the construction of the super Poisson-Lie T-dual sigma models by means of Drinfel’d superdoubles
Consequences of the isometry symmetry in string theory [10, 11]–[14]
We have obtained the solution of the equations of motion for a super non-Abelian T-dual sigma model in curved background by the super Poisson-Lie T-duality
Summary
Let us briefly review the construction of the super Poisson-Lie T-dual sigma models by means of Drinfel’d superdoubles. The super Poisson-Lie dualizable sigma models can be formulated on a Drinfel’d superdouble D ≡ (G, G) [30], a Lie supergroup whose D admits a decomposition D = G ⊕Ginto a pair of sub-superalgebras maximally isotropic with respect to a supersymmetric and ad-invariant non-degenerate bilinear form < . Where E0+(e) is a constant matrix and Π(g) defines the super Poisson structure on the Lie supergroup G, and the sub-matrices a(g) and b(g) are constructed in terms of the bilinear forms as ai j(g) = < g−1Xi g , Xj >, bij(g) = < g−1Xig , Xj >. We shall present an example of (2|2)−dimensional super non-Abelian T-dual sigma models with a curved background for which the sigma model can be explicitly solved by the super Poisson-Lie T-duality transformations This model is obtained from the Drinfel’d superdouble (C11 + A) , I(2|2)
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