(SNS Ph.D. a.y. 2017/18-2020/21)


Graduate course on Supergravity for first Ph.D. students at Scuola Normale

Lectures delivered at SISSA (2006/07-2009/10) at the EPFL (Spring 2009), at the LACES School 2009 and LACES 2021, at the SEPnet (Queen Mary, Uni. Southampton, Royal Holloway, Spring 2010) and at the Scuola Normale Superiore (Pisa, Winter 2011, Winter 2018 and Winter 2019).

The LACES 2021 lectures are also visible on YouTube.

Lecture Notes

Lecture notes are available from Springer

On this page I will collect typo corrections.


  • Introduction
    Motivations. A rapid summary of global susy.
  • Gravity as a gauge theory
    Cartan's formalism; Vielbeine; Local Lorentz; Spin connection with and without torsion; 1st order, 2nd order, 1.5 order formalism; Spinors in curved spacetime.
  • Global vs. local supersymmetry
    Promoting local supersymmetry in the Wess-Zumino model; The gravitino.
  • N=1 supergravity in 4 dimensions
    The action and susy rules; Adding a cosmological constant; Mass in Anti de Sittter; How to construct an action: Noether method, superfield method, superconformal method and the Rheonomic approach.
  • Matter couplings
    Matter multiplets; Kaehler covariant derivatives; Scalar sigma model; Scalar potential, superpotentials and D-terms; Gradient flow relations and supersymmetric Ward identities.
  • Susy breaking
    Supergravity vacua; Susy breaking scales; Rigid limits; The super-Higgs mechanism; No-scale models; Gravity mediation; The Polonyi model.
  • The duality group
    Electric-magnetic duality; Symplectic group and U-duality group; Scalar manifolds of extended supergravities.
  • Extended supergravities
    Multiplets and scalar manifolds; N=2 supergravity; Partial supersymmetry breaking.
  • Gauged supergravities
    Non abelian gauge groups in supergravity; The gauging and the scalar potential