We discuss the topological properties of a two-dimensional free Abelian gauge theory in the framework of BRST cohomology. We derive the conserved and nilpotent BRST and co-BRST charges and express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. It is because of the topological nature of the free U(1) gauge theory that the Laplacian operator goes to zero whe...

We demonstrate that the celebrated Stückelberg formalism is modified in case of a massive four (3 + 1)-dimensional (4D) Abelian 2-form theory due to presence self-duality discrete symmetry theory. The latter entails upon 4D gauge become model Hodge within framework Becchi–Rouet–Stora–Tyutin (BRST) where there existence set (anti-)co-BRST transformations corresponding usual nilpotent (anti-)BRST...

We provide a generalization of the horizontality condition of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to obtain the nilpotent (anti-)BRST symmetry transformations for all the fields of a four (3 + 1)-dimensional interacting 1-form U(1) gauge theory (QED) within the framework of the augmented superfield formalism. In the above interacting gauge theory, there i...

The classical formal equivalence upon a redefinition of the gauge connection between Chern-Simons theory and topological massive Yang-Mills theory in three-dimensional Euclidean spacetime is analyzed at the quantum level within the BRST formulation of the Equivalence Theorem. The parameter controlling the change in the gauge connection is the inverse λ of the topological mass. The BRST differen...

A crucial property of the standard antifield-BRST cohomology at non negative ghost number is that any cohomological class is completely determined by its antifield independent part. In particular, a BRST cocycle that vanishes when the antifields are set equal to zero is necessarily exact. This property, which follows from the standard theorems of homological perturbation theory, holds not only ...

In our previous papers, we prove the no-ghost theorem without light-cone directions (hep-th/0005002, hep-th/0303051). We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OC...

Starting from the covariant action for W3 gravity constructed in [1], we discuss the BRST quantization of W3 gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld–Sokolov reduction for Sl(3, IR). Nilpotency of this charge leads to the KPZ formula for W3. In the conformal gauge, where the covariant action reduces to a Toda action, the BRST...

The BRST cohomology analysis of Lian and Zuckerman leads to physical states at all ghost number for c < 1 matter coupled to Liouville gravity. We show how these states are related to states at ghost numbers zero(pure vertex operator states – DK states) and ghost number one(ring elements) by means of descent equations. These descent equations follow from the double cohomology of the String BRST ...

We show that the Floer cohomology and quantum cohomology rings of the almost Kähler manifold M , both defined over the Novikov ring of the loop space LM , are isomorphic. We do it using a BRST trivial deformation of the topological A-model. The relevant aspect of noncompactness of the moduli of pseudoholomorphic instantons is discussed. It is shown nonperturbatively that any BRST trivial deform...