BRST Invariant Effective Action Research Articles

A precisely feasible gauged model of chiral boson with its BRST cohomological perspectives

We find that Siegel type chiral boson with a parameter-dependent Lorentz non-covariant masslike term for the gauge fields to be equivalent to the chiral Schwinger model with one parameter class of Faddeevian anomaly if the model is described in terms of Floreanini–Jackiw type chiral boson. By invoking the Wess–Zunino field gauge-invariant reformulation is made. It has been shown that the gauge-invariant model has the same physical content as its gauge non-invariant ancestor had. The BRST invariant effective action corresponding to this model has also been constructed. All the nilpotent symmetries associated with the BRST symmetry along with the bosonic, ghost, and discrete symmetries have been systematically studied. We establish that the nilpotent charges corresponding to these symmetries resemble the algebra of the de Rham cohomological operators in differential geometry. In the environment of conserved charges associated with the models, we study the Hodge decomposition theorem on the compact manifold.

Radiative corrections in 2 + 1 dimensional supergravity

Supergravity in 2 + 1 dimensions has a set of first-class constraints that result in two bosonic and one fermionic gauge invariances. When one uses Faddeev–Popov quantization, these gauge invariances result in four fermionic scalar ghosts and two bosonic Majorana spinor ghosts. The BRST invariance of the effective Lagrangian is found. As an example of a radiative correction, we compute the phase of the one-loop effective action in the presence of a background spin connection, and show that it vanishes. This indicates that unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no dynamical generation of a topological mass in this model. An additional example of how a BRST invariant effective action can arise in a gauge theory is provided in Appendix B where the BRST effective action for the classical Palatini action in 1 + 1 dimensions is examined.

The BRST-invariant effective action of shadows, conformal fields, and the AdS/CFT correspondence

We study the completely symmetric, arbitrary-spin, massless and massive fields propagating in anti-de Sitter space. Using the de Donder-type gauge for such fields, we obtain a Lagrangian invariant under the global BRST transformations. We use this Lagrangian to calculate the vacuum partition function and the effective action. We show that the effective action calculated for the nonnormalizable solution of the field equations of motion with the Dirichlet boundary value problem coincides with the BRST-invariant effective action of a shadow. In the case of massless fields, the logarithmic divergence of the effective action results in a simple expression for the BRST-invariant Lagrangian of an arbitrary-spin conformal field. We show that the Nakanishi-Lautrup fields appearing in the BRST-invariant action of conformal fields can be interpreted geometrically as the boundary values of massless fields in anti-de Sitter space.

Membrane solitons as solitary waves of nonlinear string dynamics

Families of solutions to the field equations of the covariant BRST invariant effective action of membrane theory are constructed. The equations are discussed in a double-dimensional reduction; they lead to a nonlinear equation for a one-dimensional extended object. One family of solutions of these equations are solitary waves with several properties of solitonic solutions in integrable systems, providing evidence that in this double-dimensional reduction the nonlinear equations are an integrable system. The other family of solutions found exploits the property that the nonlinear system under some assumptions is equivalent to a nonlinear Schrödinger equation.

To Restore the Broken Symmetry in the Nonconfining Schwinger Model

A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored in two different ways. One of these two leads to a BRST-invariant effective action. An equivalent gauge-invariant theory is reformulated even in the usual phase space also.

BRST quantization of non-abelian BF topological theories

The off-shell nilpotent BRST charge and the BRST invariant effective action for non-abelian BF topological theories over D-dimensional manifolds are explicitly constructed. These theories have the feature of being reducible with exactly D - 3 stages of reducibility. The adequate extended phase space including the different levels of ghosts for ghosts is explicitly obtained. Using the structure of the resulting BRST charge we show that for topological BF theories the semi-classical approximation completely describes the quantum theory. The independence of the partition function on the metric also follows from our explicit construction in a straightforward way.

Quantization of a U(1) gauged chiral boson in the Batalin-Fradkin-Vilkovisky scheme.

The scheme developed by Batalin, Fradkin, and Vilkovisky (BFV) to convert a second-class constrained system to a first-class one (having gauge invariance) is used in the Floreanini-Jackiw formulation of the chiral boson interacting with a U(1) gauge field. Explicit expressions of the BRST charge, the unitarizing Hamiltonian, and the BRST invariant effective action are provided and the full quantization is carried through. The spectra in both cases have been analyzed to show the presence of the proper chiral components explicity. In the gauged model, Wess-Zumino terms in terms of the Batalin-Fradkin fields are identified.

BRST symmetry in the general gauge theories

By using the residual gauge symmetry interpretation of BRST invariance we have constructed a new BRST formulation for general gauge theories including those with open algebras. For theories with open gauge algebra the formulation leads to a BRST invariant effective action which does not contain any higher order terms in the ghost fields.

Gauge fixing in extended phase space and path integral quantization of systems with second class constraints

A new formulation of dynamical systems with second class constraints as pure gauge theories in an enlarged phase space is presented. The BRST invariant effective action for the gauge invariant version of the system is constructed. The explicit reduction on the path integral to the original phase space variables is done. Application to topologically massive electrodynamics in 3D is briefly discussed.

Canonical covariant quantization of the Brink-Schwarz superparticle.

A method for the covariant canonical quanitzation of a wide class of gauge theories with reducible first- and second-class constraints which includes the Brink-Schwarz superparticle is obtained. The application to the Brink-Schwarz superparticle is discussed in detail. The canonical Batalin-Fradkin-Vilkovisky construction of the correct Becchi-Rouet-Stora-Tyutin (BRST) operator and the BRST-invariant effective action is presented and shown to agree with the expressions obtained by Kallosh and Bergshoeff using other methods. The correct gauge-fixing procedure to recover the Brink-Schwarz superparticle action is discussed.