We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology in the case of twodimensional free U(1) gauge theory. In addition to the usual BRST charge, we deduce a conserved and nilpotent dual-BRST charge under which the gauge-fixing term remains invariant. This charge is the analogue of the adjoint(dual) exterior derivative of differential geometry. The BRST extended Casimir operator, correspon...

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator Q for the Lie algebra cohomology induced by BRST generator Q. We also po...

To exhibit the possible origin of the inner complexity of the Berkovits's pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0–brane) in its spinor moving frame or twistor-like Lorentz harmonics formulation. The presence of additional twistor-like variables (spinor harmonics) allows us to separate covariantly the first and the second class con...

We show how to relate the parafermions that occur in the W 3 string to the standard construction of parafermions. This result is then used to show that one of the screening charges that occurs in parafermionic theories is precisely the non-trivial part of the W 3 string BRST charge. A way of generalizing this pattern for a W N string is explained. This enables us to construct the full BRST char...

Based on the extended BRST formalism of Batalin, Fradkin and Vilkovisky, we perform a general algebraic analysis of the BRST anomalies in superstring theory of Neveu-Schwarz-Ramond. Consistency conditions on the BRST anomalies are completely solved. The genuine super-Virasoro anomaly is identified with the essentially unique solution to the consistency condition without any reference to a parti...

We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies à la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local f...

The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are taken into account by using the Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann surfaces to quantum mechanical variables on which BRST transformations act. The familiar ghos...

We consider a BRST approach to G/H coset WZNW models, i.e. a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and ...

We discuss some of the key topological features of a two (1 + 1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy momentum tensor, topological invariants, etc., by exploiting the on-shell nilpotent BRST-and co-BRST ...

The worldsheet sigma-model of the superstring in AdS5×S 5 has a one-parameter family of flat connections parametrized by the spectral parameter. The corresponding Wilson line is not BRST invariant for an open contour, because the BRST transformation leads to boundary terms. These boundary terms define a cohomological complex associated to the endpoint of the contour. We study the cohomology of ...