In this Letter, we propose a model which is equivalent to the Yang-Mills theory at long distances but for which all symmetries are realized linearly. On top of the gauge and Fadeev-Popov ghosts fields, the model presents several massive fields, all of which can be merged in a unique vector field with support in a curved superspace. The equivalence of this model with the gauge-fixed Yang-Mills theory is shown to result from the decoupling of these extra massive modes at small momenta. Most of the symmetries of Yang-Mills theory, including the famous BRST symmetry, can be interpreted in this way as isometries of the superspace.
The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer $W_{2,s}$ strings, where the BRST charge is written as $Q_B=Q_0+Q_1$. Using this method, we reconstruct the nilpotent BRST charges $Q_{0}$ for the integer $W_{2,s}$ strings and the half-integer $W_{2,s}$ strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the half-integer $W_{2,s}$ strings for the cases of $s=3/2$, 5/2, and 7/2.
An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class systems based on homological arguments is proposed. The general formalism is exemplified on the Freedman-Townsend model.
We derive the various forms of BRST symmetry using Batalin-Fradkin-Vilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory.
In this paper, we construct the nilpotent Becchi-Rouet-Stora-Tyutin($BRST$) charges of spinor non-critical $W_{2,s}$ strings. The cases of $s=3,4$ are discussed in detail, and spinor realization for $s=4$ is given explicitly. The $BRST$ charges are graded.
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.
Implementing the requirement that a field theory be invariant under Schwinger-Dyson BRST symmetry in the Hamiltonian formalism, we show the equivalence between Hamiltonian and Lagrangian BRST-formalism at the path integral level. The Lagrangian quantum master equation is derived as a direct consequence of the Fradkin-Vilkovisky theorem in Hamiltonian BRST quantisation.
We analyze the relation between the Lagrangian and Hamiltonian BRST symmetry generators for a recently proposed two-dimensional symmetry. In particular it is shown that this symmetry may be obtained from a canonical transformation in the ghost sector in a gauge independent way.
New BRST-invariant states for SU(3) gauge field theory are presented. The states have finite norms and unlike the states that are usually used to derive path integrals, they break SU(3) symmetry by choosing preferred gauge directions. This symmetry breaking may also give effective masses to some of the gauge bosons of the theory.
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST…
The topological field theories associated with affine Lie superalgebras are constructed. Their BRST symmetry is characterised by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators are grouped into BRST doublets. The relation between the models constructed and non-critical string theories is explored.
We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the dynamical non-Abelian 2-form gauge theory within the framework of geometrical superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian densities that respect the above nilpotent symmetry transformations. We discuss, furthermore, this (anti-) BRST invariance in the language of the superfield formalism. One of the novel features of our investigation is the observation that, in addition to the horizontality condition, we have to invoke…
In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of "dual-BRST symmetry" in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent…
In this work we present a proof of the discreteness of the spectrum for bosonic membrane, in a flat minkowski space. This may be useful to show the quantum mechanical consistence of others bosonics extended models. This proof includes the BRST residual symmetry and was directly performed over the discretized membrane model. The BRST residual invariant effective action is explicity constructed.
We present a new collective field formalism with two rather than one collective field to derive the antifield formalism for extended BRST invariant quantisation. This gives a direct and physical proof of the scheme of Batalin, Lavrov and Tyutin, derived on algebraic grounds. The importance of the collective field in the quantisation of open algebras in both the BRST and extended BRST invariant way is stressed.
The presence of a BRST symmetry in topologically twisted gauge theories makes a precise analysis of these theories feasible. While the global BRST symmetry suggests that correlation functions of BRST exact observables vanish, this decoupling might be obstructed due to a contribution from the boundary of field space. Motivated by divergent BRST exact observables on the Coulomb branch of Donaldson-Witten theory, we put forward a new prescription for the renormalization of correlation functions on the Coulomb branch. This renormalization is based on the relation between Coulomb branch integrals a…
The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicity of the BRST current.
An irreducible Hamiltonian BRST quantization method for reducible first-class systems is proposed. The general theory is illustrated on a two-stage reducible model, the link with the standard reducible BRST treatment being also emphasized.
The BFV-BRST Hamiltonian quantization method is presented for the theories where the gauge parameters are restricted by differential equations. The general formalism is exemplified by the Maxwell-like theory of symmetric tensor field.
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 antiBRST 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-L…
Our goal in this work is to present the variational method of fictitious parameters and its connection with the BRST symmetry. Firstly we implement the method in QED at zero temperature and then we extend the analysis to GQED at finite temperature. As we will see the core of the study is the general statement in gauge theories at finite temperature, assigned by Tyutin work, that the physics does not depend on the gauge choices, covariant or not, due to BRST symmetry.
An all orders algebraic proof of the multiplicative renormalizability of the novel formulation of the Gribov-Zwanziger action proposed in Phys. Rev. D 86, 045005 (2012) [arXiv:1205.3934], and allowing for an exact but spontaneously broken BRST symmetry, is provided.
A short rewiev of covariant quantization methods based on BRST-antiBRST symmetry is given. In particular problems of correct definition of Sp(2) symmetric quantization scheme known as triplectic quantization are considered.
The geometric interpretation of the antibracket formalism given by Witten is extended to cover the anti-BRST symmetry. This enables one to formulate the quantum master equation for the BRST--anti-BRST formalism in terms of integration theory over a supermanifold. A proof of the equivalence of the standard antibracket formalism with the antibracket formalism for the BRST--anti-BRST symmetry is also given.
We propose a generalisation of the Faddeev-Popov trick for Yang-Mills fields in the Landau gauge. The gauge-fixing is achieved as a genuine change of variables. In particular the Jacobian that appears is the modulus of the standard Faddeev-Popov determinant. We give a path integral representation of this in terms of auxiliary bosonic and Grassman fields extended beyond the usual set for standard Landau gauge BRST. The gauge-fixing Lagrangian density appearing in this context is local and enjoys a new extended BRST and anti-BRST symmetry though the gauge-fixing Lagrangian density in this case i…
We present several forms in which the BRST transformations of QCD in covariant gauges can be cast. They can be non-local and even not manifestly covariant. These transformations may be obtained in the path integral formalism by non standard integrations in the ghost sector or by performing changes of ghost variables which leave the action and the path integral measure invariant. For different changes of ghost variables in the BRST and anti-BRST transformations these two transformations no longer anticommute.
Recently a new formalism has been developed for the covariant quantization of superstrings. We study properties of Dp-branes and p-branes in this new framework, focusing on two different topics: effective actions and boundary states for Dp-branes. We present a derivation of the Wess-Zumino terms for super (D)p-branes using BRST symmetry. To achieve this we derive the BRST symmetry for superbranes, starting from the approach with/without pure spinors, and completely characterize the WZ terms as elements of the BRST cohomology. We also develope the boundary state description of Dp-branes by anal…
We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of "modified triplectic algebra" in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coup…
We give an introduction to rigid supersymmetry, supergravity and superspace by considering a quantum mechanical model. We analyze the constraints in superspace in this simplified model, and compare the Hamiltonian and Lagrangian BRST formalism.
We generalize the method of superfield Lagrangian BRST quantization in the part of the gauge-fixing procedure and obtain a quantization method that can be considered as an alternative to the Batalin - Vilkovisky formalism.
We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
We consider possible superfield representations of extended BRST symmetry for general gauge theories within the principle of gauge-fixing based on a generating equation for the gauge functional. We examine admissible superfield choices for an extended antibracket and delta-operator with given algebraic properties and show that only one of these choices is compatible with the requirement of extended BRST symmetry realized in terms of supertranslations along Grassmann coordinates. We demonstrate that this realization leads to the gauge-independence of the S-matrix.
We provide a BRST symmetric version of Yokoyama's Type I gaugeon formalism for quantum electrodynamics; the similar theory by Izawa can be considered as a BRST symmetrized Type II theory. With the help of the BRST symmetry, Yokoyama's physical subsidiary conditions are replaced by the Kugo-Ojima type condition. As a result, the formalism becomes applicable even in the background gravitational field. We show how the Hilbert spaces of standard formalism in various gauges are embedded in the single Hilbert space of the present formalism. We also give a path integral derivation of the Lagrangian.
In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large $N$ limit, the difference between two precursors is a BRST exact and ghost-free term. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that this BRST ambiguity has the right number of parameters t…
The complete structure of the $WG_2$ algebra is obtained from an explicit realization by an abstract Virasoro algebra and a free boson field. We then construct its BRST operator and find a seven-parameter family of nilpotnt BRST operators. These free parameters are related to the canonical transformations of the ghost, antighost fields which leave the total stress-energy tensor and the antighost field $b$ invariant.
We show the existence of a co(dual)-BRST symmetry for the usual BRST invariant Lagrangian density of an Abelian gauge theory in two dimensions of space-time where a U(1) gauge field is coupled to the Noether conserved current (constructed by the Dirac fields). Under this new symmetry, it is the gauge-fixing term that remains invariant and the symmetry transformations on the Dirac fields are analogous to the chiral transformations. This interacting theory is shown to provide a tractable field theoretical model for the Hodge theory. The Hodge dual operation is shown to correspond to a discrete s…
The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket-antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.
The status of the `BRST-invariant' condensate of mass dimension two in QCD is explained. The condensate is only invariant under an `on-shell' BRST symmetry which includes a partial gauge-fixing. The on-shell BRST symmetry represents the residual gauge symmetry under gauge transformations which preserve the partial gauge fixing. The gauge-invariant operators which correspond to the BRST-invariant condensate are identified in the Lorentz and maximal Abelian gauges and are shown to be invariant under the residual gauge transformations.
We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3 + 1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-) BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST…
We study topological Yang-Mills-Higgs theories in two and three dimensions and topological Yang-Mills theory in four dimensions in a unified framework of superconnections. In this framework, we first show that a classical action of topological Yang-Mills type can provide all three classical actions of these theories via appropriate projections. Then we obtain the BRST and anti-BRST transformation rules encompassing these three topological theories from an extended definition of curvature and a geometrical requirement of Bianchi identity. This is an extension of Perry and Teo's work in the topo…
The basic BRST cohomological properties of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in detail. It is shown that any non-trivial co-cycle from the local BRST cohomology group can be taken to stop at antighost number three, its last component belonging to the cohomology of the exterior longitudinal derivative and containing non-trivial elements from the (invariant) characteristic cohomology.
We scrutinize the many known forms of BRST symmetries, as well as some new ones, realized within a prototypical first-class system. Similarities and differences among ordinary BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetries are highlighted and discussed. We identify a precise $\mathbb{Z}_4\times\mathbb{Z}_2$ discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST transformations. Considering a Hamiltonian approach, those symmetries can be interrelated by canonical transformations among ghost variables. However, the distinguished character…
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 closed algebra is presented. In contrast to a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off shell realization of the extended algebra in a superspace with two Grassmann coordinates is obtained. The example of the Yang Mills theory is also considered.
The correspondence between BRST and unfolded formulations of field equations on group manifolds and homogeneous spaces is described. The previously introduced nonstandard BRST operator, that underlies Sp(2M) invariant higher-spin field equations, is shown to admit a natural oscillator-like realization. The coordinate independent form of conserved currents in the Sp(2M) invariant higher-spin theory is derived from the BRST formulation on Sp(2M) extended by the Heisenberg group.
After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov copies. A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between $τ$ and the gauge parameter $ω$ defined by $τ(x) = f( A_μ^ω(x))$ is ``globally single valued'', where $f( A_μ^ω(x)) = 0 $ specifies the gauge condition. As an example of the theory which satisfies this criterion, we comment on a soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, …
We describe the procedure of dimensional reduction of massless fields in $(D+1)$ dimensional Minkowski space to massive ones in $D$ dimensions in the first-quantized setting. The procedure is compatible with Lagrangian and in a straightforward way determines the inner product for massive fields. Howe duality and the extensive usage of BRST formalism allows to keep the description concise. We consider both bosonic and fermionic mixed-symmetry fields.
In this paper we analyse the ABJM theory in ${\cal N}=1$ superspace. Firstly we study the linear and non-linear BRST transformations for the ABJM theory. Then we derive the finite field dependent version of these BRST (FFBRST) transformations. Further we show that such FFBRST transformations relate the generating functional in linear gauge to the generating functional in the non-linear gauge of ABJM theory.
The issue of the BRST symmetry in presence of the Gribov horizon is addressed in Euclidean Yang-Mills theories in the Landau gauge. The positivity of the Faddeev-Popov operator within the Gribov region enables us to convert the soft breaking of the BRST invariance exhibited by the Gribov-Zwanziger action into a non-local exact symmetry, displaying explicit dependence from the non-perturbative Gribov parameter. Despite its non-locality, this symmetry turns out to be useful in order to establish non-perturbative Ward identities, allowing us to evaluate the vacuum expectation value of quantities …
The Einstein-Hilbert action in the context of Higher derivative theories is considered for finding out 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 …
In this short note we extend the results of Alfaro and Damgaard on the origin of antifields to theories with a gauge algebra that is open or reducible.
We determine the nilpotent BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho--Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We propose also a modified version of the new Maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory.
The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for second class constraints and a pair of the respective anti-BRST charges. Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly, the the BRST-anti-BRST algebra must involve a central element, related to the nonvanishing part of the constraint commutator and having no direct analogue in a first class theory. The unitarizing Hamiltonian is …
We study the twisted version of the supersymmetric $G/T=SU(n)/U(1)^{\otimes(n-1)} gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological field theory, that is, the topological matter system in the K.Li's theory of 2 dimensional gravity for the case of $n=2$, and its generalization for $n \geq 3$.
The non-perturbative nilpotent exact BRST symmetry of the Gribov-Zwanziger action in the Landau gauge constructed in [ arXiv:1506.06995 [hep-th]] is generalized to the case of Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. The resulting diagonal gluon propagator is evaluating in dimensions D=4,3,2. In D=4,3 a decoupling type behavior is found in the infrared region, while in D=2 a scaling type behavior emerges.
We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum mas…
The finite field dependent BRST (FFBRST) technique generally interrelates two different gauge fixed theories. Here we propose a new and unique FFBRST transformation that transforms the effective theory in Lorenz gauge, which represents perturbative or deconfined phase of QCD to massive gauge theory. The exercise serves two purposes. First is of course that it is a distinct connection where one of the theories is not gauge fixed and BRST invariant therefore, it is expected to give newer insights into FFBRST technique itself. Second is that a particular case of this transformation holds a novel …
