BRS Invariance Research Articles

Supersymmetric DBI equations in diverse dimensions from the BRS invariance of a pure spinor superstring

We examine the BRS invariance of the open pure spinor superstring in the presence of background superfields on a Dp-brane. It is shown that the BRS invariance leads not only to boundary conditions on the spacetime spinors, but also to supersymmetric DBI equations of motion for the background superfields on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI equations for a D9-brane.

Antiself-dual Yang–Mills, modified Faddeevs–Jackiw formalism and hidden BRS invariance

We analyze the constraints for a system of antiself-dual Yang–Mills (ASDYM) equations by means of the modified Faddeev–Jackiw method in [Formula: see text] and [Formula: see text] gauges à la Yang. We also establish the Hamiltonian flow for ASDYM system through the hidden BRS invariance in both the gauges. Finally, we remark on the bi-Hamiltonian nature of ASDYM and the compatibility of the symplectic structures therein.

The Jackiw–Pi model: Classical theory

The massive even-parity non-Abelian gauge model in three space–time dimensions proposed by Jackiw and Pi is studied at the tree-level. The propagators are computed and the spectrum consistency is analyzed, besides, the symmetries of the model are collected and established through BRS invariance and Slavnov–Taylor identity. In the Landau gauge, thanks to the antighost equations and the Slavnov–Taylor identity, two rigid symmetries are identified by means of Ward identities. It is presented here a promising path for perturbatively quantization of the Jackiw–Pi model and a hint concerning its possible quantum scale invariance is also pointed out.

BRS ‘Symmetry’, prehistory and history

Prehistory - Starting from 't Hooft's (1971) we have a short look at Taylor's and Slavnov's works (1971-72) and at the lectures given by Rouet and Stora in Lausanne-1973 which determine the transition from pre-history to history. History - We give a brief account of the main analyses and results of the BRS collaboration concerning the renormalized gauge theories, in particular the method of the regularization independent, algebraic renormalization, the algebraic proof of S-matrix unitarity and that of gauge choice independence of the renormalized physics. We conclude this report with a suggestion to the crucial question: what could remain of BRS invariance beyond perturbation theory.

The Jackiw–Pi model and its symmetries

The non-Abelian gauge model proposed by Jackiw and Pi, which generates an even-parity mass term in three spacetime dimensions, is revisited in this communication. All the symmetries of the model are collected and established by means of BRS invariance and Slavnov–Taylor identity. The path for the perturbatively quantization of the Jackiw–Pi model, through the algebraic method of renormalization, is presented.

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we proof the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft--Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredient we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory.

The BRS invariance of noncommutative Yang–Mills theory at the one-loop level

We show that U(N) Yang-Mills theory on noncommutative Minkowski space-time can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov-Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order $\hbar$, for the MS renormalized noncommutative U(N) Yang-Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.

Sum rules for e+e− → W+W− helicity amplitudes from BRS invariance

BRS invariance of the electroweak gauge theory leads to relationships between amplitudes with external massive gauge bosons and amplitudes where some of these gauge bosons are replaced with their corresponding Nambu-Goldstone bosons. Unlike the equivalence theorem, these identities are exact at all energies. In this paper we discuss such identities which relate the process e + e − → W + W − to W ± χ ∓ and χ + χ − production. By using a general form factor decomposition for e + e − → W + W −, e + e − → W ± χ ∓ and e + e − → χ + χ −, amplitudes, these identities are expressed as sum rules among scalar form factors. Because these sum rules may be applied order by order in perturbation theory, they provide a powerful test of higher order calculations. By using additional Ward-Takahashi identities we find that the various contributions are divided into separately gauge-invariant subsets, the sum rules applying independently to each subset. After a general discussion of the application of the sum rules we consider the one-loop contributions of scalar-fermions in the Minimal Supersymmetric Standard Model as an illustration.

BRS Invariance of Unoriented Open-Closed String Field Theory

We present the full action for the unoriented open-closed string field theory which is based on the \alpha=p^+ HIKKO type vertices. The BRS invariance of the action is proved up to the terms which are expected to cancel the anomalous one-loop contributions. This implies that the system is invariant under the gauge transformations with open and closed string field parameters up to the anomalies.

BRS symmetry versus supersymmetry in Yang-Mills-Chem-Simons theory

We prove that three-dimensional N = 1 supersymmetric Yang-Mills-Chem-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.

Gauge invariant formulation of strong WW scattering

Models of strong WW scattering in the s-wave can be represented in a gauge invariant fashion by defining an effective scalar propagator that represents the strong scattering dynamics. The σ( qq → qqWW) signal may then be computed in U-gauge from the complete set of tree amplitudes, just as in the standard model, without using the effective W approximation (EWA). The U-gauge “transcription” has a wider domain of validity than the EWA, and it provides complete distributions for the final state quanta, including experimentally important jet distributions that cannot be obtained from the EWA. Starting from the usual formulation in terms of unphysical Goldstone boson scattering amplitudes, the U-gauge transcription is verified by using BRS invariance to construct the complete set of gauge and Goldstone boson amplitudes in R Σ gauge.

Renormalizability of quantum gravity near two dimensions

We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from full diffeomorphism invariance. We study the Ward-Takahashi identities to determine the general structure of the counter terms. We prove to all orders that the counter terms can be supplied by the coupling and the wave function renormalization of the tree action. The bare action can be constructed to be of the Einstein action form which ensures full diffeomorphism invariance.

BRS invariance, asymptotic freedom and color confinement (a review)

It is proved that color confinement is an inevitable consequence of BRS invariance and asymptotic freedom inherent in quantum chromodynamics. BRS invariance is used to interpret or define color confinement and asymptotic freedom provides an essential means to prove it. It is also pointed out that introduction of renormalization is an essential step toward this proof and that renormalization group serves as the most useful tool in reaching the destination.

Algebraic renormalization of N = 1 supersymmetric gauge theories

The complete renormalization procedure of a general N = 1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free “algebraic renormalization” procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general non-abelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is restricted to the space of the “gauge invariant operators”, i.e. to the cohomology classes of the gauge BRS operator.

ALGEBRAIC RENORMALIZATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER

We study the algebraic renormalization of N=2 supersymmetric Yang-Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, so it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides unphysical renormalizations of the quantum fields, we find that the only coupling constant of N=2 supersymmetric Yang-Mills theories can get quantum corrections. Moreover, we prove that all the symmetries defining the theory are algebraically anomaly-free.

CONFINEMENT OF QUARKS AND GLUONS II

It is shown that color confinement is a consequence of BRS invariance and asymptotic freedom of quantum chromodynamics. BRS invariance is exploited to define color confinement, and asymptotic freedom is utilized to prove it. The proof presented in this paper is an extension of the one in the preceding paper.

Rigid invariance as derived from BRS invariance: the abelian Higgs model

Consequences of a symmetry, e.g.\ relations amongst Green functions, are renormalization scheme independently expressed in terms of a rigid Ward identity. The corresponding local version yields information on the respective current. In the case of spontaneous breakdown one has to define the theory via the BRS invariance and thus to construct rigid and current Ward identity non-trivially in accordance with it. We performed this construction to all orders of perturbation theory in the abelian Higgs model as a prelude to the standard model. A technical tool of interest in itself is the use of a doublet of external scalar ``background'' fields. The Callan-Symanzik equation has an interesting form and follows easily once the rigid invariance is established.

Canonical symmetry of a constrained Hamiltonian system and canonical ward identity

An algorithm for the construction of the generators of the gauge transformation of a constrained Hamiltonian system is given. The relationships among the coefficients connecting the first constraints in the generator are made clear. Starting from the phase space generating function of the Green function, the Ward identity in canonical formalism is deduced. We point out that the quantum equations of motion in canonical form for a system with singular Lagrangian differ from the classical ones whether Dirac's conjecture holds true or not. Applications of the present formulation to the Abelian and non-Abelian gauge theories are given. The expressions for PCAC and generalized PCAC of the AVV vertex are derived exactly from another point of view. A new form of the Ward identity for gauge-ghost proper vertices is obtained which differs from the usual Ward-Takahashi identity arising from the BRS invariance.

Flow equations and BRS invariance for Yang-Mills theories

Flow equations describe the evolution of the effective action Γ k in the process of varying an infrared cutoff k. The presence of the infrared cutoff explicitly breaks gauge and hence BRS invariance. We derive modified Slavnov-Taylor identities, which are valid for nonvanishing k. They guarantee the BRS invariance of Γ k for k → 0, and hence allow the study of non-abelian gauge theories by integrating the flow equations. Within a perturbative expansion of Γ k , we derive an equation for a k dependent mass term for the gauge fields implied by the modified Slavnov-Taylor identities.

Removal of divergences with the Batalin-Vilkovisky formalism

We show how to remove the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable, i.e. involving infinitely many parameters) in the contex of the Batalin-Vilkovisky formalism. We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of the parameters of the classical Lagrangian (possibly infinitely many) and a canonical transformation (in the sense of Batalin and Vilkovisky) of fields and BRS sources. Gauge-invariance is turned into a suitable quantum generalization of BRS invariance. We define quantum observables in this formal context and study their properties. We show the independence of the on-shell physical amplitudes from gauge fixing. We apply the result to renormalizable gauge-field theories that are gauge-fixed with a non-renormalizable gauge fixing and prove that their predictivity is retained. A corollary is that topological field theories are predictive.