Symmetries of perturbed conformal field theories

The symmetries of perturbed conformal field theories are analysed. We explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field. We also study the behaviour of D-branes under current-current bulk deformations. We find that the branes always continue to preserve as much symmetry as they possibly can, i.e. as much as is preserved in the bulk. We illustrate these findings with several examples, including permutation branes in WZW models and B-type D-branes in Gepner models