Abstract

Quantum groups are deformations of algebras which often appear in two dimensional physics. In QFT , for example, they appear in integrable RG flows satisfying the Yang Baxter relation; in CFT , they play a role in the crossing kernel of Virasoro blocks and in the fusion rules of some WZW models. However, contrary to what happens on the lattice, these quantum groups do not normally appear as global symmetries, in the sense that they do not act on operators. I will show what it means for a CFT to have the quantum group Uq(sl2) as a global symmetry. As an example, I will work out a CFT arising from the Uq(sl2) symmetric XXZ spin chain with non-local boundary conditions. I will explain how this can be studied with Coulomb gas techniques, and show its relation to unitary theories, by showing that in special cases this CFT admits subsectors which are twisted versions of minimal models.