Lectures on supergravity

These notes are based on lectures presented at the 2001 Les Houches Summerschool ``Unity from Duality: Gravity, Gauge Theory and Strings''

This is a personally colored account of the history behind N=4 Yang-Mills Theory.

An introduction to Seiberg-Witten theory and its relation to theories which include gravity.

In these lectures I will discuss the following topics: (1) Twistors in 4 flat dimensions: Massless particles; constrained phase space (x,p) versus twistors; Physical states in twistor space. (2) Introduction to 2T-physics and derivation of 1T-physics holographs and twistors: Emergent spacetimes & dynamics, holography, duality; Sp(2,R) gauge symmetry, constraints, solutions and (d,2); Global symmetry, quantization and the SO(d,2) singleton. (3) Twistors for particle dyna...

This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less rigorously, but all too often offers little insight to the uninformed reader. Instead we opted for a smooth exposition of the successive themes, choosing an order and an approach which are close to the way these pieces of mathematics could have be...

We present a short review of the group-geometric approach to supergravity theories, from the point of view of recent developments. The central idea is the unification of usual diffeomorphisms, gauge symmetries and supersymmetries into superdiffeomorphisms in a supergroup manifold. The example of $N=1$ supergravity in $d=4$ is discussed in detail, and used to illustrate all the steps in the construction of a group manifold action. In the Appendices we summarize basic notions o...

We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realiz...

In this contribution, we present the geometric approach to supergravity. In the first part, we discuss in some detail the peculiarities of the approach and apply the formalism to the case of pure supergravity in four space-time dimensions. In the second part, we extend the discussion to theories in higher dimensions, which include antisymmetric tensors of degree higher than one, focussing on the case of eleven dimensional space-time. Here, we report the formulation first intr...

These four lectures, addressed to an audience of graduate students in experimental high energy physics, survey some of the basic concepts in string theory. The purpose is to convey a general sense of what string theory is and what it has achieved. Since the characteristic scale of string theory is expected to be close to the Planck scale, the structure of strings probably cannot be probed directly in accelerator experiments. The most accessible experimental implication of sup...

This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D>4 --Lovelock gravity. It is then shown that in o...