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from Part II - Applications
Published online by Cambridge University Press: 14 November 2024
From the unique N = 1 11-dimensional supergravity, all the other supergravities in lower dimensions are thought to be obtained. To obtain the seven-dimensional gauged supergravity, we first describe a first-order formulation of 11-dimensional supergravity. Then, we describe a nonlinear ansatz, leading to a consistent truncation. The concepts of consistent truncation and nonlinear ansatze are described, and the linearized ansatz on S4 and the spherical harmonics on S4 are reviewed. Relatedly, we describe the Lagrangians and transformation rules for the (maximal) N = 8 d = 4, N = 8 d = 5, and N = 4 d = 7 gauged supergravities, the massive type IIA 10-dimensional supergravity, type IIB 10-dimensional supergravity, and some general properties of gaugings, in particular the non-compact ISO(7) gauging. We end with modified supergravities: the one with SO(1, 3) × SU(8) local Lorentz covariance in 11 dimensions, the generalization known as exceptional field theory, and the geometric approach to supergravity, in particular d'Auria and Fré’s 11-dimensional supergravity with OSp(1|32) invariance.
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