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

Abstract

Abstract We revisit non-Abelian T-duality for non-semisimple groups, where it is well-known that a mixed gravitational-gauge anomaly leads to $$\sigma $$ σ -models that are scale, but not Weyl-invariant. Taking into account the variation of a non-local anomalous term in the T-dual $$\sigma $$ σ -model of Elitzer, Giveon, Rabinovici, Schwimmer and Veneziano, we show that the equations of motion of generalized supergravity follow from the $$\sigma $$ σ -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.