A field theoretical realization of topological gravity is discussed in the semirigid geometry context. In particular, its topological nature is given by the relation between deRham cohomology and equivariant BRST cohomology and the fact that all but one of the physical operators are BRST-exact. The puncture equation and the dilaton equation of pure topological gravity are reproduced, following ...

The Hamilton-Jacobi formalism was applied to quantize the front-form Schwinger model. The importance of the surface term is discussed in detail. The BRST-anti-BRST symmetry was analyzed within Hamilton-Jacobi formalism. On leave of absence from Institute of Space Sciences, P.O BOX, MG-23, R 76900 MagureleBucharest, Romania, E-mail: [email protected] E-Mail: [email protected]

The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson ∗Also at Centro de Estudios Cient́ıficos de Santiago, Casilla 16443, Santiago 9, Chile

The BRST quantization of the null spinning string for different number of supersymmetries is given. A null spinning string with manifest space-time conformal invariance is constructed. Its BRST quantization gives negative critical dimensions for N = 0 and reproduces previous results for N = 0.

Using the generalized Hamiltonian method of Batalin, Fradkin and Vilkovsky we develop the BRST formalism for the bosonic string on AdS5×S formulated as principal chiral model. Then we show that the monodromy matrix and non-local charges are BRST invariant.

We study the BRST cohomology within a local conformal Lagrangian eld theory model built on a two dimensional Riemann surface with no boundary. We deal with the case of the complex structure parametrized by Beltrami di erential and the scalar matter elds. The computation of all elements of the BRST cohomology is given.

The topological eld theories associated with a ne Lie superalgebras are constructed. Their BRST symmetry is characterised by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators are grouped into BRST doublets. The relation between the models constructed and non-critical string theories is explored.

We discuss the algebraic way of solving the descent equations corresponding to the BRST consistency condition for the gauge anomalies and the Chern–Simons terms on a nontrivial bundle. The method of decomposing the exterior derivative as a BRST commutator is extended to the present case.

All the BRST-invariant operators in pure spinor formalism in d = 10 can be represented as BRST commutators, such as V = {Qbrst, θ+ λ+ V } where λ+ is the U(5) component of the pure spinor transforming as 1 5 2 . Therefore, in order to secure non-triviality of BRST cohomology in pure spinor string theory, one has to introduce “small Hilbert space” and “small operator algebra” for pure spinors, a...