A manifestly super-Poincaré covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a manifestly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor fo...

Recently, the superstring was covariantly quantized using the BRST-like operator Q = λ α d α where λ α is a pure spinor and d α are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and η 0 ghost. This map is then used to relate physical vertex operat...

Algebraic properties of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated to twisted gauge occurring in $\ensuremath{\kappa}$-Poincar\'e invariant theories on $\ensuremath{\kappa}$-Minkowski space are investigated. We find that BRST operation invariance action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent operation, leading algebra...

We study topological Yang-Mills-Higgs theories in two and three dimensions and topological Yang-Mills theory in four dimensions in a unified framework of superconnections. In this framework, we first show that a classical action of topological Yang-Mills type can provide all three classical actions of these theories via appropriate projections. Then we obtain the BRST and anti-BRST transformati...

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field an...

We consider the Feigin-Fuchs-Felder formalism of the SU(2)k×SU(2)l/SU(2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST invar...