Supergravity

Graduate course on supergravity for first-year Ph.D. students at the Scuola Normale Superiore.

Lectures delivered at SISSA (2006/07–2009/10), at EPFL (spring 2009), at the LACES School 2009 and LACES 2021, at SEPnet (Queen Mary, University of Southampton, Royal Holloway, spring 2010) and at the Scuola Normale Superiore (Pisa, winter 2011, 2018 and 2019).

The LACES 2021 lectures are on YouTube.

The lecture notes became the book Supergravity: From First Principles to Modern Applications (Springer). Corrections are collected on the book page.

1. Introduction

   Motivations. A rapid summary of global supersymmetry.

2. Gravity as a gauge theory

   Cartan’s formalism; vielbeins; local Lorentz; spin connection with and without torsion; 1st-order, 2nd-order and 1.5-order formalism; spinors in curved spacetime.

3. Global vs. local supersymmetry

   Promoting local supersymmetry in the Wess–Zumino model; the gravitino.

4. N = 1 supergravity in four dimensions

   The action and supersymmetry rules; adding a cosmological constant; mass in anti-de Sitter; how to construct an action: Noether method, superfield method, superconformal method and the rheonomic approach.

5. Matter couplings

   Matter multiplets; Kähler-covariant derivatives; scalar sigma model; scalar potential, superpotentials and D-terms; gradient-flow relations and supersymmetric Ward identities.

6. Supersymmetry breaking

   Supergravity vacua; supersymmetry-breaking scales; rigid limits; the super-Higgs mechanism; no-scale models; gravity mediation; the Polonyi model.

7. The duality group

   Electric–magnetic duality; symplectic group and U-duality group; scalar manifolds of extended supergravities.

8. Extended supergravities

   Multiplets and scalar manifolds; N = 2 supergravity; partial supersymmetry breaking.

9. Gauged supergravities

   Non-abelian gauge groups in supergravity; the gauging and the scalar potential.