BRS Symmetry Research Articles

ANOMALIES OF BRS AND ANTI-BRS WARD-IDENTITIES IN N=1 SUPERSYMMETRIC THEORY

The requirement of BRS and anti-BRS symmetries in N=1 supersymmetric theory leads to Ward-identities independent of the gauge parameter. The cohomology conditions are immediately satisfied. This yields a supersymmetric formula of the chiral anomaly.

On the quantization of membrane theories

In connection with the quantization of membrane theories, a three-dimensional analogue of the conformal gauge is formulated on the basis of a non-linear gauge condition. The resulting action consists of polynomials in the membrane variables and Faddeev-Popov ghosts up to quartic terms, and it preserved the BRS symmetry. Some of the applications of this formulation are briefly discussed.

The variational approach to the Kaluza-Klein theory

The canonical quantisation approach to the Kaluza-Klein theory is presented. In the case of the five-dimensional Kaluza-Klein theory the BRS symmetry for the cylindrical gauge is constructed. The temperature-dependent variational method based on the Bogoliubov inequality is developed. The instability of the Kaluza-Klein vacuum above a certain temperature T0 is shown.

Beltrami parametrization and string theory

By introducing Beltrami differentials to describe the conformal structure of the worldsheet, we prove the factorization of two-dimensional diffeomorphisms and of the corresponding BRS symmetry which is relevant for the string theory. Weyl invariance appears as a fundamental symmetry of the problem. Factorization of the connected tree diagrams is proven.

Schwinger terms and Slavnov-Taylor identities

A systematic treatment of the Schwinger terms is attempted by gauging the relevant symmetry. The Slavnov-Taylor identity arising from the BRS symmetry plays a central role in this approach. We also present a direct derivation of the Virasoro algebra from the (anomalous) Slavnov-Taylor identity by converting the Weyl anomaly into a spurious reparametrization anomaly.

Weyl gauge fixing and BRS symmetry in string theory

The Weyl freedom in string theory is incorporated into the BRS symmetry in the conformal-type gauge fixing. This clarifies the origins of the requirements such as D = 26 and the intercept condition. The physical equivalence of the reparametrization invariant and Weyl invariant path integral measures at D = 26 is established. The anomaly associated with the BRS transformation is explicitly evaluated, and the possible theory at D < 26 from the BRS viewpoint is also briefly discussed.

BRS symmetry of supergravity in superspace and its projection to component formalism

The BRS symmetry of supergravity theories is geometrically constructed in superspace. The construction is formally identical to the one which holds for gauge theories coupled to gravity. If the classical superspace constraints associated to a given set of auxiliary fields are known it is possible to obtain by projection the whole set of BRS transformation laws in component formalism. We illustrate the method with various representations of N = 1, D = 4 Poincaré supergravity. In particular we consider couplings of Chern-Simons forms. Our analysis proves the absence of U(1) anomaly in the new minimal supergravity for any coupling of matter fields.

BRS Hamiltonian quantization of a spinless relativistic particle in relativistic gauges

The mechanics of a spinless relativistic particle is quantized by using the covariant hamiltonian path integral of Balatin, Fradkin, and Vilkovisky (BFV). The local noninternal symmetry of he classical theory is fixed by using a “relativistic gauge” via BRS symmetry, a single derivation of the BFV path integral based on the underlying hamiltonian theory is given, and the boundary conditions on the path integral are determined by the BRS invariance requirement. The resulting path integral is explicitly evaluated to yield the Klein-Gordon propagator.

On the free bosonic string field theory for D≠26

The free bosonic string field action is constructed for D≠26 which is invariant under off-mass-shell gauge transformations generalizing the standard BRS symmetry for D=26. Reduction of this model upon the gauge fixing procedure is analysed and an obstacle in imposing Virasoro gauge conditions is identified with the appearance of extra degrees of freedom.

Gauge fixing for gravity-coupled theories and the super-Higgs effect beyond the unitary gauge

A straightforward gauge-fixing procedure is presented for a general gauge theory coupled to gravity, which relies on the geometrical nature of the BRS symmetry. It promotes the Stueckelberg “auxiliary” field (and its generalizations) to the level of a fundamental quantum field, like ghosts and antighosts. In this way, the Nielsen-Kallosh phenomenon is fully clarified, and a complete derivation of the quantum lagrangian of N = 1, D = 4 “new minimal” supergravity is given. As an output we analyze the super-Higgs effect beyond the unitary gauge and find a particularly simple gauge analogous to the 't Hooft-Feynman one for spontaneously broken Yang-Mills theories.

BRS invariance of the interacting Polyakov string

The modification to the BRS symmetry of Polyakov's string required to ensure the invariance of the generating functional and the decoupling of spurious states in the presence of interactions is calculated.

Stochastic equations for gravity

The Langevin equations governing stochastic quantization of gravity are established. These equations hold true, independently of the value of the torsion. They are covariant under the BRS symmetry associated to local diffeomorphisms and Lorentz transformations. The method determines simultaneously the Langevin equations of the diffeomorphisms and Lorentz ghosts, and of the classical vielbein and spin connection.

Quasi-Yang-Mills structure for the open bosonic string

Using the description of bosonic open strings by a double p-form, the ghost-auxiliary field spectrum is derived algebraically, as well as the BRS symmetry, of the free bosonic string theory. A quasi-Yang-Mills structure emerges, where lagrangians and possible anomalies are related to invariant exterior forms of higher rank. The passage from the free case to the interacting one necessitates the understanding of vortex operators defined so as to ensure some geometrical Jacobi-Bianchi identities.

Stochastic dynamics of Faddeev-Popov ghosts

The Langevin equations which determine the stochastic quantization for the complete quartet of tields of the Yang-Mills theory are constructed. The BRS symmetry is enforced at each value of the stochastic time. This defines the non-perturbative dynamics of the Faddeev-Popov ghosts.

Faddeev-Popov Ghosts and BRS Symmetry in String Theories

On decrit les coordonnees fantomes de Faddeev-Popov qui apparaissent dans la quantification covariante des cordes bosoniques et des supercordes dans l'ancien formalisme

Hamiltonian analysis of gauge theories with interacting p-forms

We display the hamiltonian analysis of gauge theories involving interacting p-form gauge fields. This yields a phase space interpretation of the spatial and temporal components of the whole pyramidal spectrum of ghosts, antighosts and generalized Stückelberg fields which one introduces in lagrangian theory. The general expression of the canonical BRS generator is displayed and its geometrical relevance is stressed. It generically involves higher order ghost interactions. The successive structure functions of the hamiltonian formalism are linked to the field strength components which are set to zero in the lagrangian theory in order to express the BRS symmetry. The method is illustrated with several examples of such higher rank systems.

A simple algebraic construction of the symmetries of supergravity

We display a direct construction of the complete BRS symmetry of a simple N = 1 supergravity. Unlike the Noether construction, this method separates the determination of the symmetry and the construction of an invariant lagrangian. The Wess and Zumino consistency condition is made explicit, providing a firm ground for the study of supergravitational anomalies.

The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories

We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.

Extended BRS symmetry in quantum gravity

The superspace formulation for BRS and anti-BRS symmetry, which has been successfully applied to ordinary and supersymmetric Yang-Mills theories, is extended to the case of quantum gravity. The action, which is constructed in the same way as in the previous cases, yields in component notation the known expressions for the gauge-fixing and Faddeev-Popov ghost terms.

Massive tensor fields in Kaluza-Klein theory and BRS symmetry

The BRS symmetry of massive tensor fields is derived through the dimensional reduction technique in the five-dimensional Kaluza-Klein theory. The physical S-matrix unitary for the massive tensor fields is established in the same way as the Kugo-Ojima formalism of the Yang-Mills theory.