Derives ten-dimensional Type IIA supergravity by dimensionally reducing D=11 supergravity on a circle: the eleven-dimensional metric splits into a ten-dimensional metric, a Kaluza-Klein vector, and a dilaton, while the three-form potential splits into a ten-dimensional three-form and a two-form, with the eleven-dimensional gravitino descending to two ten-dimensional Majorana-Weyl gravitini of opposite chirality. Because coordinate reparametrizations mix the circle direction into ten-dimensional gauge transformations, the reduced two-form's field strength must be replaced by a Chern-Simons-corrected field strength obeying a modified Bianchi identity to remain gauge invariant, and a Weyl rescaling of the metric (introducing the dilaton factor) converts the reduced action into the conventional string-frame Type IIA action. The concept belongs to supergravity / superstring theory, connecting the NS-NS sector (metric, B-field, dilaton) and R-R sector (vector, three-form) of Type IIA string theory to eleven-dimensional supergravity fields.
Derives ten-dimensional Type IIA supergravity by dimensionally reducing D=11 supergravity on a circle: the eleven-dimensional metric splits into a ten-dimensional metric, a Kaluza-Klein vector, and a…