Supergravity

(Ph.D. a.y. 2006/07-2011/12)

Where

Graduate course on Supergravity for first year Ph.D. students at SISSA (Trieste) during a.y. 2006/07-2009/10.

Lectures delivered also at the EPFL (Spring 2009), at the LACES School 2009 and at the SEPnet (Queen Mary, Uni. Southampton, Royal Holloway, Spring 2010) and at the Scuola Normale Superiore (Pisa, Winter 2011).

Lecture notes of this course will be soon available in Springer's Lecture Notes Monographs. Stay tuned!

Syllabus

  • 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