Peter C. West

Introduction to Supersymmetry and Supergravity

The publication of the first edition of “Introduction to Supersymmetry and Supergravity” was a remarkable success. This second edition contains a substantial amount of new material especially on two-dimensional supersymmetry algebras, their irreducible representations as well as rigid and local (i.e. supergravity) theories of 2-dimensional supersymmetry both in x-space and superspace. These theories include the actions for the superstring and the heterotic string. In addition, a chapter is devoted to a discussion on superconformal algebras in two dimensions and contains an account of super operator product expansion.

The Complete N=2, D=10 Supergravity

The alternative N = 2, d = 10 supergravity, which is not derivable by dimensional reduction from the N = 1, d = 11 theory, is constructed at the full non-linear level. The transformation laws of the component fields and the equations of motion are derived and shown to be consistent. The derivation makes use of superspace techniques and exploits the fact that the scalars belong to the coset space SU(1,1)/U(1).

Symmetries and Transformations of Chiral N=2 D=10 Supergravity

An SU(1,1) symmetry is identified in chiral N = 2, D = 10 supergravity. Complete supersymmetry transformation formulas are obtained for each of the fields in the theory in a covariant formalism with manifest global SU(1,1) and local U(1) symmetries.

E_11 and M Theory

We argue that 11-dimensional supergravity can be described by a nonlinear realization based on the group E11. This requires a formulation of 11-dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.

An alternative minimal off-shell version of N = 1 supergravity

Abstract A new formulation of N = 1 Poincare supergravity is presented with an axial vector A μ and an antisymmetric tensor a μν as auxiliary fields. The theory has a local U(1) chiral gauge invariance with δA μ = ϖ μ Λ and δϕ μ = − Λγ 5 ϕ μ , and a vector gauge invariance with δa μν = ϖ μ β ν − ϖ ν β μ . The auxiliary fields then provide six off-shell degrees of freedom and are thus a minimal set.

A Class of Finite Four-Dimensional Supersymmetric Field Theories

Abstract A class of N = 2 supersymmetric models consisting of N = 2 Yang-Mills coupled to N = 2 matter is shown to be finite to all orders of perturbation theory. For this to hold, the representation of the matter fields must be chosen to give a vanishing one-loop β-function. General N = 2 supersymmetric models have a β-function that is determined to all orders in perturbation theory by the one-loop contribution.

E11 and M theory

We argue that 11-dimensional supergravity can be described by a nonlinear realization based on the group E11. This requires a formulation of 11-dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.

Conformal Invariance in N=4 Supersymmetric Yang-Mills Theory

Abstract It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.

Duality Invariant Actions and Generalised Geometry

A bstractWe construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action.

Hidden superconformal symmetry in M-theory

The bosonic sectors of the eleven-dimensional and IIA supergravity theories are derived as non-linear realisations. The underlying group includes the conformal group, the general linear group and as well as automorphisms of the supersymmetry algebra. We discuss the supersymmetric extension and argue that Osp(1/64) is a symmetry of M-theory. We also derive the effective action of the closed bosonic string as a non-linear realisation.