Structure of supergravity theories

A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super W-Riemann surfaces. On these surfaces a connection is constructed. The zero curvature condition leads to the super Ward identities of the underlying supergravity. This is accomplished through the symplectic form linked to the (super)symplecti...

Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a conclusive way. In this first of three papers we do a systematic analysis of the possibilities for almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry bu...

The purpose of my PhD thesis is to investigate different group theoretical and geometrical aspects of supergravity theories. To this aim, several research topics are explored: On one side, the construction of supergravity models in diverse space-time dimensions, including the study of boundary contributions, and the disclosure of the hidden gauge structure of these theories; on the other side, the analysis of the algebraic links among different superalgebras related to superg...

The coupling of matter to supergravity with $N=1$ supersymmetry in $d=4$ dimensions is described in a geometric manner by K\"ahler superspace. A straightforward way to implement K\"ahler superspace is via $\mathrm{U}(1)$ superspace by identifying the $\mathrm{U}(1)$ pre-potential with the K\"ahler potential, which is a function of the matter (chiral) superfields. In this framework, the components of the supergravity multiplet are contained in the supervielbein and torsion ten...

We study two-dimensional N=2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity.

We conduct a systematic search for anomaly-free six-dimensional N=1 chiral supergravity theories. Under a certain set of restrictions on the allowed gauge groups and the representations of the hypermultiplets, we enumerate all possible Poincare and gauged supergravities with one tensor multiplet satisfying the 6D anomaly cancellation criteria.

In this review we show that a Clifford algebra possesses a unique irreducible representation; the spinor representation. We discuss what types of spinors can exist in Minkowski space-times and we explain how to construct all the supersymmetry algebras that contain a given space-time Lie algebra. After deriving the irreducible representations of the superymmetry algebras, we explain how to use them to systematically construct supergravity theories. We give the maximally supers...

The topic of 4D, N = 1 supersymmetry is introduced for the reader with a prior background in relativistic quantum field theory. The presentation is designed to be a useful primer for those who plan to later engage in serious investigation of the area or as an overview for the generally interested.

These notes give a summary of lectures given in Corfu in 2010 on basic ingredients in the study of supergravity. It also summarizes initial chapters of a forthcoming book `Supergravity' by the same authors.

We present a geometrical description of N=8 supergravity, using central charge superspace. The essential properties of the multiplet, like self-duality properties of the vectors or the non-linear sigma model structure of the scalars, are found as consequences of constraints at 0 and 1/2 canonical dimension. We also present in detail how to derive from this geometrical formulation the supergravity transformations as well as the whole equations of motion for the component field...