Research Specifications

We show that the WZW model on the Heisenberg Lie group H_4 has Poisson–Lie symmetry only when the dual Lie group is A2⊕2A1. In this way, we construct the mutual T-dual sigma models on Drinfel’d double generated by the Heisenberg Lie group H_4 and its dual pair, A2⊕2A1, as the target space in such a way that the original model is the same as the H_4 WZW model. Furthermore, we show that the dual model is conformal up to two-loop order. Finally, we discuss D-branes and the worldsheet boundary conditions defined by a gluing matrix on the H4WZW model. Using the duality map obtained from the canonical transformation description of the Poisson–Lie T-duality transformations for the gluing matrix which locally defines the properties of the D-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group H_4 and its dual model.