Generalised geometry #4: The Courant bracket and the Jacobiator

The Courant bracket In addition to the generalised tangent bundle, the next fundamental structure of generalised geometry is the bilinear, skew-symmetric bracket called the Courant bracket. The Courant bracket is defined on the sections of $latex {E = TM \oplus T^{\star}M}&fg=000000$ such that it is the generalised analogue of a standard Lie bracket for vector-fields …

Doubled diffeomorphisms and the generalised Ricci curvature

I was asked a question the other week about the idea of doubled diffeomorphisms, such as those found in double field theory. A nice way to approach the concept is to start with dualised linearised gravity [1]. That is to say, we start with a theory considering only the field $latex h_{ij}(x^{\mu}, x^a, \tilde{x}_a) &fg=000000 …

Double Field Theory: The Courant Bracket

1. Introduction In this post we are going to briefly and somewhat schematically discuss the appearance of the Courant bracket in Double Field Theory (DFT), following [1]. The point here is mainly to set the stage, so we jump straight into motivating the Courant bracket. In the next post, we will then study the B-transformations …