T-duality in massive integrable field theories: the homogeneous and complex sine-Gordon models

The T-duality symmetries of a family of two-dimensional massive integrable field theories defined in terms of asymmetric gauged Wess–Zumino–Novikov–Witten actions modified by a potential are investigated. These theories are examples of massive non-linear sigma models and, in general, T-duality relates two different dual sigma models perturbed by the same potential. When the unperturbed theory is self-dual, the duality transformation relates two perturbations of the same sigma model involving different potentials. Examples of this type are provided by the homogeneous sine-Gordon theories, associated with cosets of the form G/U(1)r where G is a compact simple Lie group of rank r. They exhibit a duality transformation for each element of the Weyl group of G that relates two different phases of the model. On-shell, T-duality provides a map between the solutions to the equations of motion of the dual models that changes Noether soliton charges into topological ones. This map is carefully studied in the complex sine-Gordon model, where it motivates the construction of Bogomol'nyi-like bounds for the energy that provide a novel characterisation of the already known one-solitons solutions where their classical stability becomes explicit.