E. Cremmer

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.

The SO(8) supergravity

We present the derivation of the SO(8) supergravity theory by dimensional reduction of the supergravity theory in 11 dimensions to 4 dimensions. It has been found that the equations of motion are invariant under the global non-compact group E7(+7). They can be derived from a family of Lagrangians invariant under a local compact group SU(8). The general procedure to deal with non-compact global internal symmetry without introducing ghosts is discussed in connection with the appearance of an associated compact local symmetry and the use of a non-linear realization of the non-compact group. The supersymmetry transformation rules have been partially derived by dimensional reduction; their complete form follows from the assumption of covariance with respect to E7 and SU(8). We also present briefly the O(N) supergravities N = 7, 6, 5 and explain the symmetry SU(4)×SU(1, 1) found for the O(4) supergravity.

Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect

We derive the lagrangian and transformation laws of the coupled Yang-Mills-matter-supergravity system for unextended n = 1 local supersymmetry. We study the super-Higgs effect and the normal Higgs effect of the Yang-Mills gauge group G. In the case of N chiral multiplets “minimally” coupled to supergravity, transforming according to some N-dimensional, generally reducible representation of G, we find a model-independent mass formula: Supertrace M2 = ∑J=032 (−)2J(2J+1)mJ2= (N−1)(2m322−κ2DαDα) − 2gαDαTrTα , where m32 is the gravitino mass, κ and gα the gravitational and gauge couplings, respectively, Dα is the auxiliary component of the gauge multiplet of G and Tα the generators of G in the representation of the matter chiral multiplets.

Naturally Vanishing Cosmological Constant in N=1 Supergravity

Abstract For N =1 supergravity theories we show that the choice of a particular class of Einstein spaces for the Kahler manifold of the hidden sector leads to a vanishing cosmological constant without unnatural fine tuning. The total scalar potential from the hidden and physical sector is positive definite. The resulting low energy softly broken globl supersymmetry for the matter fields is thus the same as in the case of factorized superpotential models with a flat Kahler metric.

The N = 8 supergravity theory. I. The lagrangian

Abstract The SO(8) supergravity action is constructed in closed form. A local SU(8) group as well as the exceptional group E7 are invariances of the equations of motion and of a new first order lagrangian.

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.

Dualisation of dualities

We analyse the global (rigid) symmetries that are realised on the bosonic fields of the various supergravity actions obtained from eleven-dimensional supergravity by toroidal compactification followed by the dualisation of some subset of fields. In particular, we show how the global symmetries of the action can be affected by the choice of this subset. This phenomenon occurs even with the global symmetries of the equations of motion. A striking regularity is exhibited by the series of theories obtained respectively without any dualisation, with the dualisation of only the Ramond-Ramond fields of the type IIA theory, with full dualisation to lowest degree forms, and finally for certain inverse dualisations (increasing the degrees of some forms) to give the type IIB series. These theories may be called the GLA, D, E and GLB series, respectively. It turns out that the scalar Lagrangians of the E series are sigma models on the symmetric spaces K(E11−D)⧹E11t-D (where K(G) is the maximal compact subgroup of G) and the other three series lead to models on homogeneous spaces K(G) ⧹G⋉Rs. These can be understood from the E series in terms of the deletion of positive roots associated with the dualised scalars, which implies a group contraction. We also propose a constrained Lagrangian version of the even-dimensional theories exhibiting the full duality symmetry and begin a systematic analysis of abelian subalgebras.

Vector multiplets coupled to N=2 supergravity: Super-Higgs effect, flat potentials and geometric structure

We obtain general properties of N=2 gauged extended supergravity coupled to vector multiplets, which can gauge an arbitrary group. General formulas for masses and curvatures are derived. Particular attention is devoted to the scalar potential of the theory which determines the classical vacuum structure. Explicit examples are given in which the potential is identically zero, but supersymmetry is broken. It is found that these theories are symmetric under generalized duality transformations.

Coupling Supersymmetric Yang-Mills Theories to Supergravity

Abstract We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace M 2 = Σ J (−) 2J (2J + 1)m J 2 = 2(N − 1)m 3 2 2 , where m 3 2 is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.

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.