Observables in Topological Theories: A Superspace Formulation

The BRST algebra of supergravity is characterized by two different bilinears of the commuting supersymmetry ghosts: a vector $\gamma^\mu$ and a scalar $\phi$, the latter valued in the Yang-Mills Lie algebra. We observe that under BRST transformations $\gamma$ and $\phi$ transform as the superghosts of, respectively, topological gravity and topological Yang-Mills coupled to topological gravity. This topological structure sitting inside any supergravity leads to universal equiv...

The four-dimensional topological Yang-Mills theory with two anticommuting charges is naturally formulated on K\"ahler manifolds. By using a superspace approach we clarify the structure of the Faddeev-Popov sector and determine the total action. This enables us to perform perturbation theory around any given instanton configuration by manifestly maintaining all the symmetries of the topological theory. The superspace formulation is very useful for recognizing a trivial observa...

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.

We discuss the algebraic structure of the various BRST symmetries associated with topological Yang-Mills theory as a generalization of the BRS analysis developed for the non-Abelian anomaly in the local Yang-Mills theory. We show that our BRST algebra leads to an extended {\it Russian formula\/} and {\it descent equations}, which contains the descent equation of Yang-Mills theory as sub-relations. We propose the non-Abelian anomaly counterpart in Topological Yang-Mills theory...

The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non power counting renormalizable couplings has also been worked out in any number of spacetime dimensions. This Physics Report is devoted to reviewing in a self-...

We consider a superconformal quantum mechanical system which has been chosen on the basis of a local BRST topological invariance. We suggest that it truly leads to topological observables which we compute. The absences of a ground state and of a mass gap are special features of this system.

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of the BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the ...

The antifield-BRST formalism and the various cohomologies associated with it are surveyed and illustrated in the context of Yang-Mills gauge theory. In particular, the central role played by the Koszul-Tate resolution and its relation to the characteristic cohomology are stressed.

A method for the calculation of the BRST cohomology, recently developed for 2D gravity theory and the bosonic string in the Beltrami parametrization,is generalised to the superstring theories quantized in super-Beltrami parametrization.

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.