1. General Introduction: The Ingredients of Supergravity Theories;
2. The Scalar Sector and Global Symmetries;
3. The Fermionic Sector;
4. A Worked-Out Example: Pure N = 1, D = 4 Model With Cosmological Constant;
1. Why Gauging Extended Supergravities?
2. The Gauging Procedure;
3. Restoring Duality Covariance: The Embedding Tensor;
4. General Duality Covariant Formulation of Gauged Supergravities;
5. Tensor Hierarchies;
6. The Maximal Gauged Supergravities in D = 4, Their Vacua and Higher-Dimensional
Origin.
Basic notions of general relativity in the tetrad formulation, tensor calculus and group theory.
To help prepare for Lectures 1 and 2, lecture notes [1] are provided. As for Lectures 3,4 I refer the students to the reviews [2, 3].
[1] M. Trigiante, “An Introduction to Ungauged Supergravities”, lecture notes;
[2] M. Trigiante, “Gauged Supergravities,” Phys. Rept. 680 (2017), 1-175,
doi:10.1016/j.physrep.2017.03.001 [arXiv:1609.09745 [hep-th]];
[3] H. Samtleben, “Lectures on Gauged Supergravity and Flux Compactifications,” Class.
Quant. Grav. 25 (2008), 214002 doi:10.1088/0264-9381/25/21/214002 [arXiv:0808.4076
[hep-th]].