Kaluza-Klein dimensional reduction is an indispensable ingredient of the theoretical physics, since, M-theory and superstring theories are consistent in eleven and ten dimensions and thus, to make a connection to our four-dimensional space-time physics, it is crucial to use this mechanism. Dimensional reduction on a general coset space such as a sphere, introduced by Pauli, is more subtle that that of a group manifold reduction, introduced by DeWitt, including the circle reduction of Kaluza and Klein. While there is a group-theoretic argument for the consistency of the latter, there is no such an argument for the former, hence, besides the exceptional cases, all Pauli reductions may be inconsistent. We study an uplift ansatz for two specific truncations of gauged STU supergravity. This theory itself is an important truncation of the renowned N = 8, gauged SO(8) supergravity in four dimensions. We consider two truncations of the former theory, named as 3+1 and 2+2, due to the way of truncations of their gauge fields. We find the uplift ans?tze for the metric and the four-form field strength in these cases. We consider two theories and explore the possibility of their consistent Pauli S^2 reductions. First, minimal supergravity in five dimensions, and second, the Salam-Sezgin theory. We use the Hopf reduction technique in both cases, and by that, we show while it is not possible to perform a consistent reduction of the former, there is a consistent Pauli reduction of the latter, and by this construction, we can recover the result of Gibbons-Pope in 2003. In other words, we can provide a group theoretical argument for their work. To make the latter case happen, we find a new higher dimensional origin for the Salam-Sezgin theory, at least in the bosonic sector.
Kaluza-Klein dimensional reduction is an indispensable ingredient of the theoretical physics, since, M-theory and superstring theories are consistent in eleven and ten dimensions and thus, to make a connection to our four-dimensional space-time physics, it is crucial to use this mechanism. Dimensional reduction on a general coset space such as a sphere, introduced by Pauli, is more subtle that that of a group manifold reduction, introduced by DeWitt, including the circle reduction of Kaluza and Klein. While there is a group-theoretic argument for the consistency of the latter, there is no such an argument for the former, hence, besides the exceptional cases, all Pauli reductions may be inconsistent. We study an uplift ansatz for two specific truncations of gauged STU supergravity. This theory itself is an important truncation of the renowned N = 8, gauged SO(8) supergravity in four dimensions. We consider two truncations of the former theory, named as 3+1 and 2+2, due to the way of truncations of their gauge fields. We find the uplift ans?tze for the metric and the four-form field strength in these cases. We consider two theories and explore the possibility of their consistent Pauli S^2 reductions. First, minimal supergravity in five dimensions, and second, the Salam-Sezgin theory. We use the Hopf reduction technique in both cases, and by that, we show while it is not possible to perform a consistent reduction of the former, there is a consistent Pauli reduction of the latter, and by this construction, we can recover the result of Gibbons-Pope in 2003. In other words, we can provide a group theoretical argument for their work. To make the latter case happen, we find a new higher dimensional origin for the Salam-Sezgin theory, at least in the bosonic sector.