Yang-Mills gauge anomalies in the presence of gravity with torsion

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity with torsion are discussed by using the so-called Maurer-Cartan horizontality conditions. With the help of an operator \d which allows to decompose the exterior spacetime derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms and gauge anomalies.Comment: 24 pages, report REF. TUW 94-1

Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time

Starting from a recently proposed Abelian topological model in (2+1) dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for generalization is detected. However we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore in order to quantize the theory we construct a complete set of BRST and anti-BRST equations using the horizontality condition.Comment: 8 pages. To appear in Physical Review

The BV-algebra structure of W_3 cohomology

We summarize some recent results obtained in collaboration with J. McCarthy on the spectrum of physical states in $W_3$ gravity coupled to $c=2$ matter. We show that the space of physical states, defined as a semi-infinite (or BRST) cohomology of the $W_3$ algebra, carries the structure of a BV-algebra. This BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector fields on the base affine space of $SL(3,C)$. Details have appeared elsewhere. [Published in the proceedings of "Gursey Memorial Conference I: Strings and Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys. 447, (Springer Verlag, Berlin, 1995)]Comment: 8 pages; uses macros tables.tex and amssym.def (version 2.1 or later

Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six ($4 + 2)$-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables.Comment: LaTeX file, 23 page

Algebraic structure of gravity in Ashtekar variables

The BRST transformations for gravity in Ashtekar variables are obtained by using the Maurer-Cartan horizontality conditions. The BRST cohomology in Ashtekar variables is calculated with the help of an operator $\delta$ introduced by S.P. Sorella, which allows to decompose the exterior derivative as a BRST commutator. This BRST cohomology leads to the differential invariants for four-dimensional manifolds.Comment: 19 pages, report REF. TUW 94-1

Semi-infinite cohomology of W-algebras

We generalize some of the standard homological techniques to \cW-algebras, and compute the semi-infinite cohomology of the \cW_3 algebra on a variety of modules. These computations provide physical states in \cW_3 gravity coupled to \cW_3 minimal models and to two free scalar fields.Comment: 15 page

Free Abelian 2-Form Gauge Theory: BRST Approach

We discuss various symmetry properties of the Lagrangian density of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of the theory are found to be absolutely anticommuting in nature. For our present 2-form gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of the physicality criteria where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc

Ghost Equations and Diffeomorphism Invariant Theories

Four-dimensional Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the same type as found in the topological theories for Yang-Mills fields. A peculiar feature of the gravitational theory, characterized by diffeomorphism invariance, is a direct link of vector supersymmetry with the field equation of motion for the Faddeev-Popov ghost of diffeomorphisms.Comment: LaTex, 10 pages; sign corrected in eq. (3.9); added and completed reference

The Dynamical Nonabelian Two-Form: BRST Quantization

When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a $B\wedge F$ coupling and a kinetic term for $B$ is included, the gauge field develops an effective mass. The theory can be made invariant under a non-abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST-invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both abelian and non-abelian models of mass generation.Comment: 15 pages, revte