Anomalous symmetries in Kähler geometry

We initiate a study of centrally extended ($\textit{anomalous}$) symmetries in K\"ahler geometry, focusing on the simplest, and most ubiquitous, Abelian case. In particular, we provide a local description of the geometry admitting such isometries. A long-standing no-go theorem asserts that there is an obstruction to gauging such symmetries in the purely K\"ahler framework. Utilizing the language of sypersymmetry, we then show that these symmetries may be gauged within the setup of generalized K\"ahler geometry. Our results may be applied to quotients, T-dualities, etc.