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In the paper we discuss the role of the axial U (1)A symmetry in the chiral phase transition using the U (N f )R × U (N f )L linear sigma model with two massless quark flavors. It is expected that above a certain temperature the axial U (1)A symmetry will be restored. A string-like static solution, the η string can be formed and detected in the ultrarelativistic heavy-ion collision process.

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We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.