Joel Scherk

Supergravity in theory in 11 dimensions

We present the action and transformation laws of supergravity in 11 dimensions which is expected to be closely related to the O(8) theory in 4 dimensions after dimensional reduction.

How to get masses from extra dimensions

A generalized method of dimensional reduction, applicable to theories in curved space, is described. As in previous works by other authors, the extra dimensions are related to the manifold of a Lie group. The new feature of this work is to define and study a class of Lie groups, called “flat groups”, for which the resulting theory has no cosmological constant, a well-behaved potential, and a number of arbitrary mass parameters. In particular, when the analysis is applied to the reduction of 11-dimensional supergravity to four dimensions it becomes possible to incorporate three arbitrary mass parameters in the resulting N = 8 theory. This shows that extended supersymmetry theories allow more possibilities for spontaneous symmetry breaking than was previously believed to be the case.

Supersymmetric Yang-Mills Theories

Abstract Yang-Mills theories with simple supersymmetry are constructed in 2, 4, 6, and 10 dimensions, and it is argued that these are essentially the only cases possible. The method of dimensional reduction is then applied to obtain various Yang-Mills theories with extended supersymmetry in two and four dimensions. It is found that all possible four-dimensional Yang-Mills theories with extended supersymmetry are obtained in this way.

Supersymmetry, supergravity theories and the dual spinor model

Abstract We study the connection between the dual spinor model and supersymmetry. We show that in the low-energy region, the dual spinor model yields a supersymmetric Yang-Mills theory with O(4) internal symmetry and a supergravity theory with O(4) internal symmetry.

Spontaneous Breaking of Supersymmetry Through Dimensional Reduction

A general technique for deriving consistent theories with spontaneously broken supersymmetry and massive gravitinos is illustrated by exploiting the chiral invariance of N = 1 supergravity in four dimensions to construct a theory with broken N = 2 supersymmetry in three dimensions.

Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant

The super Higgs effect is studied in the (2,32) + (12, 0+, 0−) model. The most general action is obtained using the recently developed tensor calculus: it contains an arbitrary function of two variables G(A,B), A and B being the 0+ scalar and 0− pseudoscalar fields of the matter system. The conditions are given which G must satisfy in order that both the gravitino ψμ becomes massive and no cosmological term is induced. Explicit examples are given, a class of them leading to the mass formula mA2 + mB2 = 4mψ2.

Supersymmetry, Supergravity Theories and the Dual Spinor Model

We study the connection between the dual spinor model and supersymmetry. We show that in the low-energy region, the dual spinor model yields a supersymmetric Yang-Mills theory with O(4) internal symmetry and a supergravity theory with O(4) internal symmetry.

Su(4) invariant supergravity theory

Abstract We present a new supergravity theory which is invariant under four separate local supersymmetry transformations. The action is invariant under global SU(4) transformation realized on the fields without use of the equations of motion. In addition, the equations of motion are invariant under a non-compact global SU(1,1) group. The equations of motion of this theory are shown to be equivalent to those of the previously derived SO(4) theory through a redefinition of the field variables involving duality transformations on the vector fields.

Super-higgs effect in supergravity with general scalar interactions

Using the recently established tensor calculus for supergravity, we construct the most general action for the scalar multiplet coupling. We discuss under which conditions supersymmetry is broken spontaneously and show explicitly that the gravitino acquires a mass by absorbing the Goldstone fermion. Parity violation as well as a cosmological constant can be avoided.

Spontaneously Broken N=8 Supergravity

Abstract N = 8 supergravity in five dimensions is constructed by identifying local Sp(8) and global E(6) invariances and comparing with known theories. It is then used to obtain spontaneously broken N = 8 supergravity in four dimensions with four arbitrary mass parameters.