P. van Nieuwenhuizen

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.

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.

Self-duality in odd dimensions

Abstract For spacetime dimension d = 4 k − 1 one may take the “square root” of the Proca equation for a massive antisymmetric tensor field. The result is a “self-dual” field which propagates half as many massive modes. We present a simple supersymmetric model for d = 3. We also discuss other types of odd-dimensional self-duality, in d = 4 k + 1 and in euclidean spaces.

The Auxiliary Fields of Supergravity

Abstract We solve the problem of what the minimal set of auxiliary fields of supergravity is, needed to close the gauge algebra, and present the invariant action. The result is simple: only a scalar, a pseudoscalar and an axial world vector field are needed. Our approach is closely related to superspace geometry.

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.

Quantum Inequivalence of Different Field Representations

Abstract The gauge theories of antisymmetric tensor potentials A μν and A μνϱ describe 1 and 0 degrees of freedom, respectively. Yet we show the gravitational trace anomalies of A μν and a scalar field A to be different, and that of A μνϱ to be non-vanishing. Corresponding inequivalences also occur in their one-loop counterterms when the spacetime has non-trivial topology. Furthermore, the coupling of A μνϱ to gravity provides a gauge principle derivation of the cosmological constant. Possible applications to supergravity are also discussed.

On ghost-free tensor Lagrangians and linearized gravitation

The most general linear Lagrangian for massless and massive tensor fields without ghosts and tachyons is determined. Transversality is used to eliminate massless ghosts. The linear Einstein and Fierz-Pauli Lagrangians are unique for massless and massive tensor fields containing spin two. Hence, for gravitation, as for electromagnetism, gauge invariance and locality follow from positivity of the free-field energy. Symmetric and antisymmetric tensor theories with continuous zero-mass limit are found, but contain only spin one and spin zero.

General construction of the unitary representations of anti-de sitter superalgebras and the spectrum of the S4 compactification of 11-dimensional supergravity☆

Abstract We construct the spectrum of the S4 compactification of d = 11 supergravity by simple algebraic methods. The spectrum consists of a special class of positive-energy unitary irreducible representations of the supergroup Osp (8 ∗ /4) = Osp (6, 2 4 ) , the so-called short supermultiplets. This paper shows how to obtain easily all such representations of the supergroup Osp ( 8 ∗ 4 ) . We find that there is an ultra-short supermultiplet, the doubleton, which is analogous to the singleton of Osp ( 8 4 , R ) . The method described here can be used to obtain all positive-energy unitary supermultiplets of Osp ( 8 ∗ 4) and not just those that aise in the S4 compactification.

Gauged N=8 d=5 supergravity

Abstract The complete gauged nonlinear N = 8 d = 5 supergravity action and supersymmetry transformation laws (without four- and three-fermion terms) are presented. They are obtained from the ungauged model by reinterpreting part of the field strenghts of the abelian vector fields as real self-dual second-rank antisymmetric tensors. The complete set of T-tensor identities are given and their validity is checked numerically. The model has a local Yang-Mills SO(6) and a local composite USp(8) symmetry. The self-duality is essential for the consistent coupling of the antisymmetric tensors to the nonabelian gauge fields.

Gauge Theory of the Conformal and Superconformal Group

Abstract We show that the locally scale invariant Weyl theory of gravity is the gauge theory of the conformal group. Proper conformal transformations are gauged by a non-propagating gauge field. A gauge theory for the superconformal group is obtained which is locally scale, Lorentz, and chiral invariant but not locally supersymmetric despite remarkable cancellations.