Abstract
We analyse super non-Abelian T-duality for principal chiral models, symmetric
space sigma models, and semi-symmetric space sigma models for general Lie
supergroups. This includes T-duality along both bosonic and fermionic
directions. Specifically, super non-Abelian T-duality exchanges the
Maurer-Cartan equations with the equations of motion thus mapping integrable
models into integrable models. This, in turn, allows us to construct the T-dual
Lax connections. As a prime example, we analyse the OSp(1|2) principal chiral
model, and whilst the target superspace of this model is a three-dimensional
supergravity background, we argue that its super non-Abelian T-dual falls
outside the class of such backgrounds.