Non-abelian fermionic T-duality in supergravity

A bstract Field transformation rules of the standard fermionic T-duality require isometries to anticommute, which leads complexification Killing spinors and results in complex valued dual backgrounds. We generalize field transformations setting with non-anticommuting show that resulting backgrounds are solutions double theory. Explicit examples non-abelian T-dualities produce real given. Some our can be bosonic T-dualized into usual supergravity solutions, while others genuinely non-geometric. Comparison alternative treatment based on sigma models supercosets shows consistency.