Non-abelian fermionic T-duality in supergravity

TL;DR

This paper extends fermionic T-duality to non-anticommuting isometries, producing real supergravity backgrounds and exploring their properties within double field theory, including examples of non-abelian dualities and non-geometric solutions.

Contribution

It generalizes fermionic T-duality to non-anticommuting isometries, providing explicit real background solutions and analyzing their relation to double field theory.

Findings

Explicit examples of non-abelian fermionic T-dualities producing real backgrounds.

Some dual backgrounds can be bosonic T-dualized into standard supergravity solutions.

Identification of genuinely non-geometric dual backgrounds.

Abstract

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