Topological Gravity on (D,N)−(D,N)-Shift Superspace Formulation

In this contribution, we re-assess the subject of topological gravity by following the Shift Supersymmetry formalism. The gauge-fixing of the theory goes under the Batallin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and anti-ghost superfields, associated to the super-vielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on the gauge-fixing for BF-type models

Anti-symmetric rank-2 Matter Field on Superspace for N_{T}=2

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended $N_{T}=2$ SUSY. We start off from the $N_{T}=2$, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as $Q-$exact forms, which allows us to write the energy-momentum tensor as $Q-$exact observables.Comment: 10 pages, no figure, LaTe

Superspace Gauge Fixing of Topological Yang-Mills Theories

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ``shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in orderto determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type.Comment: 26 pages, no figures, Late

Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.Comment: 27 pages, Late