On non-Abelian T-duality for non-semisimple groups

Understand

We revisit non-Abelian T-duality for non-semisimple groups, where it is well-known that a mixed gravitational-gauge anomaly leads to $\sigma$-models that are scale, but not Weyl-invariant.

• Taking into account the variation of a non-local anomalous term in the T-dual $\sigma$-model of Elitzer, Giveon, Rabinovici, Schwimmer \& Veneziano, we show that the equations of motion of generalized supergravity follow from the $\sigma$-model once the Killing vector $I$ is identified with the trace of the structure constants.
• As a result, non-Abelian T-duals with respect to non-semisimple groups are solutions to generalized supergravity.
• We illustrate our findings with Bianchi spacetimes.