Lectures on supergravity

We give an elementary introduction to the structure of supergravity theories. This leads to a table with an overview of supergravity and supersymmetry theories in dimensions 4 to 11. The basic steps in constructing supergravity theories are considered: determination of the underlying algebra, the multiplets, the actions, and solutions. Finally, an overview is given of the geometries that result from the scalars of supergravity theories.

We provide a pedagogical introduction to $N=1$ supergravity/supersymmetry in relation to particle physics. The various steps in the construction of a generic $N=1$ supergravity model are briefly described, and we focus on its low energy supersymmetric limit. The conditions for supersymmetry and supergravity breaking are investigated, and realistic mechanisms suitable for particle physics identified. We then study the model-building aspects of `softly-broken' supersymmetric ex...

In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousin...

This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the a-maximization. Part 2: a brief look at 2d N=(2,2) and N=(0,2) dynamics, covering the Landau-Ginzburg and Calabi-Yau models, the elliptic genera on T^2, and the triality of Gadde-Gukov-Putrov. Appendix: a review of basic properties of supers...

In these lectures we discuss various aspects of gauge theories with extended $N=2$ and $N=4$ supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action for the light degrees of freedom in the $N=2$ super Yang-Mills theory and the conjecture, supported by some checks, that the $N=4$ super Yang-Mills theory is dual in the sense of Montonen-Olive.

In these lectures we present a detailed description of various aspects of gauge theories with extended N=2 and N=4 supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action for the light degrees of freedom in the N=2 super Yang-Mills theory and the conjecture, supported by some checks, that the N=4 super Yang-Mills theory is dual in the sense of Montonen-Olive.

In the first part of this lecture, some very basic ideas in supersymmetry and supergravity are presented at a level accessible to readers with modest background in quantum field theory and general relativity. The second part is an outline of a recent paper of the author and his collaborators on the AdS/CFT correspondence applied to the ABJM gauge theory with $\cal{N} =8$ supersymmetry.

We present a non-geometric derivation of $\mathcal{N}$=1 Super Yang-Mills by focusing on the consistency of interactions that extend the free vector supermultiplet rather than assuming gauge invariance under extended symmetries. By utilizing a superspace first-order description, the theory is given in closed form as a third-order polynomial which includes a single cubic interaction term instead of an infinite series, thus eliminating the need for a special gauge. The geometri...

This article contains an overview of some recent attempts at understanding supergravity and string duals of four dimensional gauge theories using the AdS/CFT correspondence. We discuss the general philosophy underlying the various ways to realize Super Yang-Mills theories in terms of systems of branes. We then review some of the existing duals for N=2 and N=1 theories. We also discuss differences and similarities with realistic theories.

This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a previous Workshop of this series, and reaching only at the doorstep of the full edifice of such theories.