Norbert Dragon

Completeness and Nontriviality of the Solutions of the Consistency Conditions

Abstract For the case of a compact gauge group we determine all solutions to the consistency conditions. In particular, our results imply that the known list of anomalies is complete also for nonrenormalizable models.

All consistent Yang-Mills anomalies

Abstract For the case of a compact gauge group we list all solutions to the consistency equations which have to be satisfied by anomalies. We describe the main algebraic tools and theorems required for this complete classification. Our results answer the question whether in nonrenormalizable gauge theories there exist additional up-to-now unknown anomalies to the negative.

LIE ALGEBRA COHOMOLOGY

We calculate the cohomology of the BRS operator s modulo an auxiliary differential operator t where both operators act on invariant polynomials in anticommuting variables Ci and commuting variables Xi.Ci and Xi transform according to the adjoint representation of the Lie algebra of a compact Lie group. The cohomology classes of s modulo t are related to the solutions of the consistency equations which ha have to be satisfied by anomalies of Yang-Mills theories. The present investigation completes the proof of the completeness and nontriviality of these solutions and, as a by-product, determines the cohomology of the underlying Lie algebra.

The gravitational anomalies

Abstract We determine all solutions to the consistency equations which have to be satisfied by anomalies in gravitational theories with a Poincare-invariant ground state.

N = 2 rigid supersymmetry with gauged central charge

Abstract We develop a general setting for N = 2 rigid supersymmetric field theories with gauged central charge in harmonic superspace. We consider those N = 2 multiplets which have a finite number of off-shell components and exist off shell owing to a non-trivial central charge. This class includes, in particular, the hypermultiplet with central charge and various versions of the vector-tensor multiplet. For such theories we present a manifestly supersymmetric universal action. Chern-Simons couplings to an external N = 2 super Yang-Mills multiplet are given, in harmonic superspace, for both the linear and non-linear vector-tensor multiplets with gauged central charge. We show how to deduce the linear version of the vector-tensor multiplet from six dimensions.

Sliding scales in minimal supergravity

Abstract Supergravity models obtained by minimal covariant extension from globally supersymmetric models automatically contain sliding scales if supersymmetry is spontaneously broken. The sliding gravitino mass is not affected by quadratic divergencies. Form invariance under SU( n ,1)-transformations singles out cubic superpotentials. The supersymmetry breaking appears in the observed sector as soft F -type breaking.

BRST Symmetry and Cohomology

We present the mathematical considerations which determine all gauge invariant actions and anomaly candidates in gauge theories of standard type such as ordinary or gravitational Yang Mills theories. Starting from elementary concepts of field theory the discussion tries to be explicit and complete, only the cohomology of simple Lie algebras it quoted from the literature.

Self-interacting vector-tensor multiplet

Abstract We construct a consistent self-coupling for the vector-tensor multiplet in N =2 harmonic central charge superspace.

Symmetry Breaking of Supersymmetric SU(5)

Abstract Numerous inequivalent ground states are shown to exist in the supersymmetric SU(5) model. We derive necessary conditions for an explicit breaking of supersymmetry to yield a potential bounded from below and to select the phenomenologically desired vacuum. These requirements are fulfilled in an example.

The Higgs mechanism in N = 2 superspace

We describe the Higgs mechanism for general N = 2 super-Yang-Mills theories in a manifestly supersymmetric form based on the harmonic superspace