Beltrami parametrization and gauged BRST symmetry for the free bosonic string

The BRST symmetry for the free bosonic string in the Beltrami parametrization is gauged via a Noether procedure. The resulting local BRST symmetry is characterized by a (localized) differential algebra which is shown to be isomorphic to the (global) BRST algebra one starts from. The corresponding locally invariant gauge-fixed action which exhibits the factorization property is constructed, and a form for the (perturbative BRST current-algebra) anomaly, associated with the localized differential algebra is given. The equivalence between the Noether localization procedure presented here and a procedure which mimics the direct “geometrical” gauging of the BRST symmetry for the Yang-Mills theory is shown.     

BRST charges for finite nonlinear algebras

Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.     

BRST model for equivariant cohomology and representatives for the equivariant thom class

In this paper the BRST formalism for topological field theories is studied in a mathematical setting. The BRST operator is obtained as a member of a one parameter family of operators connecting the Weil model and the Cartan model for equivariant cohomology. Furthermore, the BRST operator is identified as the sum of an equivariant derivation and its Fourier transform. Using this, the Mathai-Quillen representative for the Thom class of associated vector bundles is obtained as the Fourier transform of a simple BRST closed element.Supported by the SV FOM/SMC Mathematical Physics, The Netherlands     

On BRST quantization of second class constraint algebras

A BRST quantization of second-class constraint algebras that avoids Dirac brackets is constructed, and the BRST operator is shown to be related to the BRST operator of first class algebra by a nonunitary canonical transformation. The transformation converts the second class algebra into an effective first class algebra with the help of an auxiliary second class algebra constructed from the dynamical Lagrange multipliers of the Dirac approach. The BRST invariant path integral for second class algebras is related to the path integral of the pertinent Dirac brackets, using the Parisi-Sourlas mechaism. As an application the possibility of string theories in subcritical dimensions is considered.     

BRST quantization of superstring field theory

We write the gauge fixed action which arises in the quantization of Witten's string field theory in a linear gauge, in a form which applies to both the superstring and the bosonic string. The corresponding BRST transformation is nilpotent only on-shell. We construct also an off-shell nilpotent BRST transformation which formally leaves invariant the quantum effective action. This BRST transformation has a geometrical interpretation which could allow to describe the gauge anomalies of the superstring field theory as the nontrivial cohomology of the BRST charge via the Wess-Zumino consistency condition.     

BRST quantization of the superparticle

We show that the quantization of the superparticle action is possible. This is done by shifts in the BRST operator and the resulting action has an infinite number of ghosts. The total BRST operator is given by an infinite sum and is shown to be nilpotent. We also obtain a BRST invariant kinetic operator that contains the dynamical, auxiliary and gauge pieces in it.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

Interacting physical states of the bosonic string. I

A preliminary discussion on the importance of the contact terms in relation with the existence of many string vacua is presented. The problem of the BRST invariance of the string states transition amplitudes is considered in the sigma model approach to the string. It is shown that the BRST invariance is controlled by a gravitational (Diff) anomaly, and its connections with the standard Virasoro constraints are illustrated. The tachyon amplitudes are analysed and the BRST invariant dilaton vertex operator for non flat world-sheet is constructed.     

Field-dependent symmetries in Friedmann–Robertson–Walker models

We consider effective actions of the cosmological Friedmann–Robertson–Walker (FRW) models and discuss their fermionic rigid BRST invariance. Further, we demonstrate the finite field-dependent BRST transformations as a limiting case of continuous field-dependent BRST transformations described in terms of continuous parameter κ$\kappa$. The Jacobian under such finite field-dependent BRST transformations is computed explicitly, which amounts an extra piece in the effective action within functional integral. We show that for a particular choice of a parameter the finite field-dependent BRST transformation maps the generating functional for FRW models from one gauge to another.     

Reducible gauge algebra of BRST-invariant constraints

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anti-commuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.     

The relationship between the gauged BRST symmetry and the ghost number symmetry

A general method of gauging the BRST algebra by combining a (local) ghost number symmetry with the standard (global) BRST algebra, is displayed. This method enables us to construct an automatically nilpotent local BRST algebra and to obtain in a straightforward way the corresponding versions of the action and the eventual anomalies. To illustrate the procedure we study the Yang-Mills and the free bosonic string theories (including the “conformal” Beltrami parametrization) and show that it reproduces the results discussed in the literature. Two major outcomes of this scheme are briefly discussed: a possible connection between ghost number and BRST currents, arising from the Slavnov identities and the implications of the ghost number anomaly for the BRST localization program in theories such as string theory.     

Investigation of the vacuum structure of the Georgi-Glashow model on the lattice

In this paper the BKS kernels of BRST bosonic strings are given. And from the kernels the relationships between geometric quantization and path integral quantization of bosonic strings with BRST symmetry are established. At the classical level, we also prove that the symplectic form in the phase space of bosonic strings is BRST invariant and nondegenerate.     

Canonical BRST quantisation of worldsheet gravities

We reformulate the BRST quantisation of chiral Virasoro and W₃ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator Q, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator Q², calculated using operator products, to the gauge fermion.     

Geometric BRST quantization,I: Prequantization

This is the first part of a two-part paper dedicated to the definition of BRST quantization in the framework of geometric quantization. After recognizing prequantization as a manifestation of the Poisson module structure of the sections of the prequantum line bundle, we define BRST prequantization and show that it is the homological analog of the symplectic reduction of prequantum data. We define a prequantum BRST cohomology theory and interpret it in terms of geometric objects. We then show that all Poisson structures correspond under homological reduction. This allows to prove, in the BRST context, that prequantization and reduction commute.     

Becchi-Rouet-Stora-Tyutin quantization and Hamiltonian formalism

An introductory review of BRST hamiltonian formalism is presented. The method of quantization of gauge and string theories is discussed. A few simple examples are presented to illustrate the BRST techniques.     

BRST current and anomalies in spinning string in background fields

Calculation of the super Jacobian of the holomorphic Becchi-Rouet-Stora-Tyutin (BRST) transformations of the path-integral functional measure of the spinning string variable and its ghosts in presence of background fields is undertaken in order to obtain BRST current identity and related anomalies. The free BRST current identity is obtained only if the background fields satisfy the equations of motion. In this case the superconformal factor decouples from the background fields and it is possible to incorporate the super Liouville action.     

Notoph gauge theory: Superfield formalism

We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the “notoph” (i.e. the opposite of “photon”) gauge field by Ogievetsky and Palubarinov way back in 1966–67. We briefly outline the problems involved in obtaining the absolute anticonimutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.     

Temperature and the critical dimension of strings

Thermofield dynamics is used to generalize the BRST invariance of strings to nonzero temperature. The requirement that the BRST generator is nilpotent implies thatd=26 even at nonzero temperature.     

On the Gauge Invariant Lagrangian for Seiberg--Witten Topological Monopoles

A topological gauge invariant Lagrangian for Seiberg--Witten monopoleequations is constructed. The action is invariant under a huge classof gauge transformations which after BRST fixing leads to the BRSTinvariant action associated to Seiberg--Witten monopole topologicaltheory. The supersymmetric transformation of the fields involved inthe construction is obtained from the nilpotent BRST algebra.     

A Consideration of BRST Cohomology in the First Quantization of RNS String

The difference of Grassmanian even-odd and degree even-odd of (super-) conformal ghosts is stressed. With some modifications in the BRST charges and the commutation relations, it can be shown that the first quantization of RNS strings allows the BRST cohomology analysis.