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1 results

  • 16 - AdS7 × S4 nonlinear KK compactification of 11-dimensional supergravity and related notions

  • from Part II - Applications
  • Horatiu Nastase, Universidade Estadual Paulista, São Paulo
  • Book:
    Introduction to Supergravity and its Applications
    Published online:
    14 November 2024
    Print publication:
    21 November 2024, pp 177-209

  • Summary

    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.