Target-space pdeudo-duality in topological sigma models

We discuss pseudoduality relations applicable to two dimensional topological sigma models and construct necessary and sufficient conditions for their existence. We outline the classical and quantum conformal symmetries for warming-up to the preliminary discussion of the subject, and see their effects in establishing our desired duality expressions. We use the power of Cartan geometry in analyzing our target space pseudoduality expressions. For this purpose, orthonormal coframing approach was adopted and all structures were pulled-back to the world-sheet to observe the impact of pseudo-duality transformations. Since a topological sigma model is based on two dimensional N = 2 supersymmetric world sheet which is mapped to the Kähler manifolds on target space, we reduced our theory to the N=1 supersymmetric one and use the corresponding conventions in the relevant chirality. In view of our findings, we show that pseudoduality between two topological sigma models could be established by means of the solutions of equations of motions which are mapped to each other. We find out that pseudoduality expressions exist only if the corresponding torsions of the target spaces vanish, and curvatures are constant and opposite to each other. This result amounts that target spaces of the pseudodual models are dual symmetric spaces which are remarkable in the sense that this transformation is geometrically produces the classical duality relations in the literature. The specialty of pseudoduality applicable to the topological sigma models appears in the equality of pseudoduality relations to the mirror symmetry in regular topological field theory.