Current algebra and generalized Cartan geometry

This article shows that the approach to generalized curvature and torsion pioneered by Poláček and Siegel [Natural curvature for manifest T-duality, .] is a generalization of Cartan geometry—rendering latter natural from the point of view of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="normal">O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>d</a:mi><a:mo>,</a:mo><a:mi>d</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:math>-generalized geometry. We present this approach in the generalized metric formalism and show that almost all parts of the additional higher generalized tensors appearing in this approach correspond to covariant derivatives of the generalized Riemann tensor. As an application, we use this framework to phrase <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>σ</f:mi></f:math>-model dynamics in an explicitly covariant way—both under generalized diffeomorphisms and local gauge transformations. Published by the American Physical Society 2024