Supergravity: The Principles

  • Pietro Giuseppe Frè


This chapter starts with a historical outline that describes the birth of supersymmetry both in String Theory and in Field Theory, touching also on the biographies and personalities of the theorists who contributed to create this entire new field through a complicated and, as usual, far from straight, path. The chapter proceeds than with the conceptual foundations of Supergravity, in particular with the notion of Free Differential Algebras and with the principle of rheonomy. Sullivan’s structural theorems are discussed and it is emphasized how the existence of p-forms, that close the supermultiplets of fundamental fields appearing in higher dimensional supergravities, is at the end of the day a consequence of the superPoincaré Lie algebras through their cohomologies. The structure of M-theory, the constructive principles to build supergravity Lagrangians and the fundamental role of Bianchi identities is emphasized. The last two sections of the chapter contain a thorough account of type IIA and type IIB supergravities in D=10, the structure of their FDAs, the rheonomic parameterization of their curvatures and the full-fledged form of their field equations.


Bianchi Identity Supergravity Theory Supersymmetry Transformation Einstein Frame Supersymmetry Algebra 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Pietro Giuseppe Frè
    • 1
  1. 1.Dipartimento di Fisica TeoricaUniversity of TorinoTorinoItaly

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