An extension of the non-local regularization scheme is formulated in the Sp(2) symmetric Lagrangian BRST quantization framework. It generates a systematic treatment of the anomalous quantum master equations and allows to subtract the divergences as well as to calculate genuine higher loop BRST and anti BRST anomalies.

The BRST formulation is used in order to derive the existence criterion for classical bi-Hamiltonian systems, based on non-anomalous deformation of the gauge-fixing structure. The recursion operator is then used to provide the entire hierarchy of integrable models associated to the original BRST and anti-BRST charges.

Using arguments based on BRST cohomology, the pure spinor formalism for the su-perstring in an AdS 5 × S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.

Using arguments based on BRST cohomology, the pure spinor formalism for the su-perstring in an AdS 5 × S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.

We show that a modification of the BRST lattice quantization allows to circumvent an old paradox, formulated by Neuberger, related to lattice Gribov copies and nonperturbative BRST invariance. In the continuum limit the usual BRST formulation is recovered. ⋆ Address until August 31st, 1998. ⋆⋆ Permanent address.

Brane-like states are defined by physical vertex operators in NSR superstring theory, existing at nonzero pictures only. These states exist both in open and closed string theories, in the NS and NS-NS sectors respectively. In this paper we present a detailed analysis of their BRST properties, giving a proof that these vertex operators are physical, i.e. BRST invariant and BRST non-trivial.

We construct the BRST operator for the non-linear WB2 and W4 algebras. Contrary to the general belief, the nilpotent condition of the BRST operator doesn’t determine all the coefficients. We find a three and seven parameter family of nilpotent BRST operator for WB2 and W4 respectively. These free parameters are related to the canonical transformation of the ghost antighost fields.

The status of the ‘BRST-invariant’ condensate of mass dimension two in QCD is explained. The condensate is only invariant under an ‘on-shell’ BRST symmetry which includes a partial gauge fixing. The on-shell BRST symmetry represents the residual gauge symmetry under gauge transformations which preserve the partial gauge fixing. The gauge-invariant operators which correspond to the BRST-invarian...

The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer W2,s strings, where the BRST charge is written as QB = Q0+Q1. In this paper, using this method, we reconstruct the nilpotent BRST charges Q0 for the integer W2,s strings and the half-integer W2,s strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the...

The detailed description of the method of the construction of the nilpotent BRST charges for nonlinear algebras of constraints appearing in the description of the massless higher spin fields on the AdSD background is presented. It is shown that the corresponding BRST charge is not uniquely defined, but this ambiguity has no impact on the physical content of the theory. BRST – BFV method [1] is ...