Lectures on supergravity

In an ungauged supergravity theory, the presence of a \emph{scalar potential} is allowed only for the minimal $\N=1$ case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking supersymmetry only through the so-called \emph{gauging procedure}. The latter consists in promoting a suitable global symmetry group to local symmetry to be gauged by the vector fields of the theory. Gauged supergravities provide a valuable approach to...

We study theories of 4D, N=1 supersymmetric massless, arbitrary higher half odd-integer superspins. A new series of such theories is found to exist for arbitrary superspin Y (Y=s+1/2 for any integer s). The lowest member (s=1) of the series is the original off-shell formulation of 4D, N=1 supergravity first presented by Breitenlohner in 1977.

In this paper I review the multiplet calculus of $N = 1$, $D = 1$ local supersymmetry with applications to the construction of models for spinning particles in background fields, and models with space-time supersymmetry. New features include a non-linear realization of the local supersymmetry algebra and the coupling to anti-symmetric tensor fields of both odd and even rank. The non-linear realization allows the construction of a $D = 1$ cosmological-constant term, which prov...

We study theories of 4D, N=1 supersymmetric massless, arbitrary integer superspins. A new state-of-the art is being established by the discovery of a new series of such theories for arbitrary superspin Y (Y=s for any integer s) The lowest member of the series is surprisingly found to be a previously established formulation of the spin (3/2, 1) supermultiplet.

These are expanded notes of lectures given at the summer school "Gif 2000" in Paris. They constitute the first part of an "Introduction to supersymmetry and supergravity" with the second part on supergravity by J.-P. Derendinger to appear soon. The present introduction is elementary and pragmatic. I discuss: spinors and the Poincar\'e group, the susy algebra and susy multiplets, superfields and susy lagrangians, susy gauge theories, spontaneously broken susy, the non-linear s...

These lectures present an introduction to AdS-CFT, and are intended both for begining and more advanced graduate students, which are familiar with quantum field theory and have a working knowledge of their basic methods. Familiarity with supersymmetry, general relativity and string theory is helpful, but not necessary, as the course intends to be as self-contained as possible. I will introduce the needed elements of field and gauge theory, general relativity, supersymmetry, s...

These Lectures have been given at Laboratori Nazionali di Frascati in the month of March, 2005. The main idea was to provide our young collegues, who joined us in our attempts to understand the structure of $N$-extended supersymmetric one-dimensional systems, with short descriptions of the methods and techniques we use. This was reflected in the choice of material and in the style of presentation. We base our treatment mainly on the superfield point of view. Moreover, we pref...

In this talk, we review how the superspace formulation of maximally supersymmetric field theories (including supergravity) naturally leads to introduction of pure spinors and pure spinor superfields, and why the formalism provides off-shell formulations. This approach to pure spinor superfields thus stresses field-theoretic aspects rather than the first-quantised ones normally used e.g. in superstring theory. We discuss how the BRST operator arises and the principles behind c...

We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8 theory, we express the full field equations for the N=1,2,4 theories in a universal form without introducing Kleinian operators. We also use a non-minimal N=4 higher spin algebra tensored with U(3) to describe a higher spin extension of N=4 super...

In these proceedings for the First School on Field Theory and Gravitation (Vit\'oria, Brasil), a brief introduction is given to superstring theory and its duality symmetries. This introduction is intended for beginning graduate students with no prior knowledge of string theory.