Spin(n, n) × ℝ+ generalised geometry and consistent truncations on branes

A bstract In this note we show how the consistent truncations on half-supersymmetric branes of Leung and Stelle and Lin, Skrzypek and Stelle fit into the general exceptional generalised geometry analysis of Cassani et al. Each solution defines a torsion-free Spin( n ) structure in the Spin( n, n ) × ℝ + generalised geometry introduced by Strickland–Constable, where n is the dimension of the space transverse to the brane. Embedding this into the appropriate exceptional generalised geometry then defines the truncation. As a by-product we derive a new consistent truncation on the IIA NS5-brane to six-dimensional 𝒩 = (2 , 0) supergravity coupled to a tensor multiplet, and new consistent truncations on the D6- and D7-branes to seven- and eight-dimensional pure half-maximal supergravity respectively.