anti-BRST Invariance Research Articles

Geometry and topology of anti-BRST symmetry in quantized Yang–Mills gauge theories

The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi–Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev–Popov quantization approach, the anti-BRST invariance reflects thoroughly the classical symmetry of the Yang–Mills theories with respect to gauge fixing methods. The Nakanishi–Lautrup field is also defined and worked out as a geometric object. This formulation helps us to introduce two absolutely new topological invariants of quantized Yang–Mills theories, so-called the Nakanishi–Lautrup invariants. The cohomological structure of the anti-BRST symmetry is also studied and the anti-BRST topological index is derived accordingly.

Anti-BRST in the Causal Approach

It is known that the elimination of anomalies in all orders of perturbation theory is an open problem. The constraints given by usual invariance properties and the Wess–Zumino identities are not enough to eliminate the anomalies in the general case of a Yang–Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of perturbation theory. So, anti-BRST transform gives nothing new, and we have to find other ideas to restrict and eventually eliminate the anomalies for a general Yang–Mills theory.

Gauge fixing invariance and anti-BRST symmetry

It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.

Construction of a massive ABJM theory without Higgs superfields

A massive Aharony-Bergman-Jafferis-Maldacena (ABJM) model in superspace is analysed by considering a Proca-type mass term into the most general Faddeev-Popov action in a covariant gauge. The presence of a mass term breaks the original BRST and anti-BRST invariance of the model. Further, the symmetry of the massive ABJM model is restored by extending the BRST and anti-BRST transformations. We show that the supergauge dependence of the generating functional for connected diagrams occurs in the presence of mass and ghost–anti-ghost condensates in the theory.

Axial symmetry, anti-BRST invariance, and modified anomalies

It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out, which yields a set of modified consistent anomalies.

Anti-BRST symmetry and background field method

We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding antiBRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from antiBRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-antiBRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolve the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N⩽3 part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.

Symmetry Invariance, Anticommutativity and Nilpotency in BRST Approach to QED: Superfield Formalism

We provide the geometrical interpretation for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) interacting U(1) gauge theory within the framework of superfield approach to BRST formalism. This interacting theory, where there is an explicit coupling between the U(1) gauge field and matter (Dirac) fields, is considered on a (4, 2)-dimensional supermanifold parametrized by the four spacetime variables x?(? = 0, 1, 2, 3) and a pair of Grassmannian variables ? and ¯? (with ?2 = ¯?2 = 0, ?¯? + ¯?? = 0). We express the Lagrangian density and (anti-)BRST charges in the language of the superfields and show that (i) the (anti-)BRST invariance of the 4D Lagrangian density is equivalent to the translation of the super Lagrangian density along the Grassmannian direction(s) (? and/or ¯?) of the (4, 2)- dimensional supermanifold such that the outcome of the above translation(s) is zero, and (ii) the anticommutativity and nilpotency of the (anti-)BRST charges are the automatic consequences of our superfield formulation. MSC 2010: 81T80, 81T13, 58J70.

Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a (4,2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresponding four (3+1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4,2)-dimensional supermanifold parametrized by the ordinary four space-time variables x µ (with µ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and $$ \bar \theta $$ (with θ 2 = $$ \bar \theta $$ 2 = 0, θ $$ \bar \theta $$ + $$ \bar \theta $$ θ = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.

Renormalizing a Becchi-Rouet-Stora-Tyutin-invariant composite operator of mass dimension 2 in Yang-Mills theory

We discuss the renormalization of a BRST and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with the general BRST and anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this study stems from a recent claim that the non-vanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with the previous works and argue the physical implications of the obtained results.

FIELD-ANTIFIELD QUANTIZATION OF THE YANG-MILLS THEORY WITH EXTENDED BRST INVARIANCE IN THE COLLECTIVE FIELD APPROACH

The collective field procedure is an interesting way of deriving the field-antifield formalism from a standard BRST approach. Trivial shift symmetries are introduced in the original gauge theory and then a judicious choice of gauge-fixing leads to the identification of the antighosts of these extra symmetries as the antifields. When explicit extended BRST invariance (BRST and anti-BRST invariance) is required, two collective fields are necessary, and the gauge-fixing structure is more complex. In this article, with the purpose of clarifying some aspects of this procedure, we consider in detail the example of the Yang–Mills theory.

Superspace formulation for the Batalin-Vilkovisky formalism with extended BRST invariance.

A superspace formulation for the Batalin-Vilkovisky formalism (also called field-antifield quantization) with extended BRST invariance (BRST and anti-BRST invariance) for gauge theories with a closed algebra is presented. In contrast with a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off-shell realizaiton of the extended algebra in a superspace with two Grassmann coordinates is obtained. The example of the Yang-Mills theory is also considered. \textcopyright{} 1996 The American Physical Society.

THE SPINNING CONFORMAL PARTICLE AND ITS BRST QUANTIZATION

We present the classical and quantum theory of the spinning conformal particle. This is a model with manifestly O(2, 4) (conformal) invariance, and it describes both massive and massless particles of arbitrary spin depending on the projection to Minkowski space. We perform both an ordinary BRST quantization and an extended one including the anti-BRST symmetry. It is shown that anti-BRST invariance is necessary to ensure ghost decoupling and make the quantization of the model consistent.

Auxialiary conditions in BRST quantization

A general structure of allowed auxiliary conditions in both ordinary and generalized BRST quantization is presented. Such conditions are shown to fall into two classes which always should imply each other. Both antiBRST invariance and coBRST invariance are shown to fit into the framework. AntiBRST invariance is also shown to imply an OSp symmetry. A previously given algorithm for solving BRST cohomologies is formulated in terms of allowed auxiliary conditions.

The geometry of quantum gauge theories: A superspace formulation of BRST symmetry

The superspace representation of BRST transformations as translations in the direction of an extra anti-commuting coordinate is reviewed. Yang-Mills theory is described in terms of a gauge superfield whose super-curvature satisfies certain constraints. We solve these curvature constraints in terms of unconstrained superspace pre-potentials and write the quantum Yang-Mills action in a form in which the BRST invariance is manifest. (Anti-BRST invariance is included by using a further anti-commuting variable). In this approach, the quantum Yang-Mills action is shown to possess an infinitely reducible pre-gauge symmetry, which must be gauge fixed.

On the consistency of a BRST quantization — The rôle of the antiBRST symmetry

The inclusion of the antiBRST symmetry in addition to the BRST symmetry in the quantization of a gauge theory is considered. It is proven that in all cases where the BRST symmetry ensures ghost decoupling, it is also permissible to impose antiBRST invariance. A general ghost decoupling theorem is furthermore proven using the BRST and antiBRST symmetry. This theorem is shown to yield ghost decoupling even in theories where the BRST symmetry by itself does not. An example of such a theory is given. There the addition of the antiBRST symmetry removes the unphysical ghost degeneracy and one finds the expected result.

EQUIVALENCE OF THE LAGRANGIAN AND HAMILTONIAN BRST CHARGES FOR THE BOSONIC STRING IN THE HARMONIC AND CONFORMAL GAUGES

We consider the BRST formalism for the bosonic string in arbitrary gauges, both from the Hamiltonian and from the Lagrangian point of view. In the Hamiltonian formulation we construct the BRST charge Q(H) following the Batalin-Fradkin-Fradkina-Vilkovisky (BFFV) formalism in phase space. In the Lagrangian formalism, we use the Noether procedure to construct the BRST charge Q(L) in configuration space. We then discuss how to go from configuration to phase space and demonstrate that the dependence of Q(L) on the gauge fixing disappears and that both charges become equal. We work through two gauges in detail: the conformal gauge and the de Donder (harmonic) gauge. In the conformal gauge one must use equations of motion, and a simple canonical transformation is found which exhibits the equivalence. In the de Donder gauge, nontrivial canonical transformations are needed. Our results overlap with work by Beaulieu, Siegel and Zwiebach on the de Donder gauge, but since we only require BRST invariance and not anti-BRST invariance, we need simpler field redefinitions; moreover, we stay off-shell.