# Antoine Van Proeyen (KU Leuven): Supergravity

## Advanced Graduate Lecture course

**Lecture Course (260091 VU): March 7 - 29, 2019**

**Time: 13:15 - 14:45**

**Start: Thursday, March 7, 2019**

**Further Dates: Friday, March 8, 2019**

**Friday, March 15, 2019**

**Thursday, March 21, 2019, Friday, March 22, 2019**

**Thursday, March 28, 2019, Friday, March 29, 2019**

**End: Friday, March 29, 2019**

**Abstract:**

Students with a basic knowledge of supersymmetry will be introduced in the basic ingredients of a supergravity theory. They will learn how to obtain an action that is invariant under a set of local supersymmetry transformations satisfying an algebra that contains general coordinate transformations. They will be introduced in the tools that are useful for constructing couplings of matter fields to the simplest supergravity theories: the superconformal calculus. In particular they will in this way obtain the basic structure of N=1 matter-coupled supergravity.

**Content of the lecture course:**

1. A few ingredients. Here could come a bit notation on the spinors, the Rarita-Schwinger field, symmetry transformations in general, and differential geometry.

2. The basic N=1 supergravity in D=4. First a repetition about first and second order formulation of general relativity and then generalizing it to the the basic N=1 supergravity in D=4.

3. Gauged spacetime translations and the superconformal group.

4. The conformal approach to pure N=1 supergravity.

5. Construction of the matter-coupled N=1 supergravity.

6. The physical N=1 matter-coupled supergravity.

**Aims for the course:**

These lectures are intended to learn the students the basic ingredients of a supergravity theory and teach them how to obtain a supergravity theory using the tools of superconformal calculus.