456 research outputs found
Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models
Recent results on the cohomological reformulation of the problem of
consistent interactions between gauge fields are illustrated in the case of the
Yang-Mills models. By evaluating the local BRST cohomology through descent
equation techniques, it is shown (i) that there is a unique local, Poincar\'e
invariant cubic vertex for free gauge vector fields which preserves the number
of gauge symmetries to first order in the coupling constant; and (ii) that
consistency to second order in the coupling constant requires the structure
constants appearing in the cubic vertex to fulfill the Jacobi identity. The
known uniqueness of the Yang-Mills coupling is therefore rederived through
cohomological arguments.Comment: 6 pages in LaTeX, ULB-PMIF/930
The sh Lie structure of Poisson brackets in field theory
A general construction of an sh Lie algebra from a homological resolution of
a Lie algebra is given. It is applied to the space of local functionals
equipped with a Poisson bracket, induced by a bracket for local functions along
the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order
maps are constructed which combine to form an sh Lie algebra on the graded
differential algebra of horizontal forms. The same construction applies for
graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket
of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.Comment: 24 pages Latex fil
Higher Derivative Chern--Simons Extensions
We study the higher-derivative extensions of the D=3 Abelian Chern--Simons
topological invariant that would appear in a perturbative effective action's
momentum expansion. The leading, third-derivative, extension I_ECS turns out to
be unique. It remains parity-odd but depends only on the field strength, hence
no longer carries large gauge information, nor is it topological because metric
dependence accompanies the additional covariant derivatives, whose positions
are seen to be fixed by gauge invariance. Viewed as an independent action,
I_ECS requires the field strength to obey the wave equation. The more
interesting model, adjoining I_ECS to the Maxwell action, describes a pair of
excitations. One is massless, the other a massive ghost, as we exhibit both via
the propagator and by performing the Hamiltonian decomposition. We also present
this model's total stress tensor and energy. Other actions involving I_ECS are
also noted.Comment: 3 typos fixed. 5 page
Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces
In the context of massless higher spin gauge fields in constant curvature
spaces, we compute the surface charges which generalize the electric charge for
spin one, the color charges in Yang-Mills theories and the energy-momentum and
angular momentum for asymptotically flat gravitational fields. We show that
there is a one-to-one map from surface charges onto divergence free Killing
tensors. These Killing tensors are computed by relating them to a cohomology
group of the first quantized BRST model underlying the Fronsdal action.Comment: 21 pages Latex file, references and comment adde
Comments on the Equivalence between Chern-Simons Theory and Topological Massive Yang-Mills Theory in 3D
The classical formal equivalence upon a redefinition of the gauge connection
between Chern-Simons theory and topological massive Yang-Mills theory in
three-dimensional Euclidean space-time is analyzed at the quantum level within
the BRST formulation of the Equivalence Theorem. The parameter controlling the
change in the gauge connection is the inverse of the topological
mass. The BRST differential associated with the gauge connection redefinition
is derived and the corresponding Slavnov-Taylor (ST) identities are proven to
be anomaly-free. The Green functions of local operators constructed only from
the (-dependent) transformed gauge connection, as well as those of
BRST invariant operators, are shown to be independent of the parameter
, as a consequence of the validity of the ST identities. The relevance
of the antighost-ghost fields, needed to take into account at the quantum level
the Jacobian of the change in the gauge connection, is analyzed. Their role in
the identification of the physical states of the model within conventional
perturbative gauge theory is discussed.Comment: 19 pages, LATEX, to appear in Journal of High Energy Physic
First order parent formulation for generic gauge field theories
We show how a generic gauge field theory described by a BRST differential can
systematically be reformulated as a first order parent system whose spacetime
part is determined by the de Rham differential. In the spirit of Vasiliev's
unfolded approach, this is done by extending the original space of fields so as
to include their derivatives as new independent fields together with associated
form fields. Through the inclusion of the antifield dependent part of the BRST
differential, the parent formulation can be used both for on and off-shell
formulations. For diffeomorphism invariant models, the parent formulation can
be reformulated as an AKSZ-type sigma model. Several examples, such as the
relativistic particle, parametrized theories, Yang-Mills theory, general
relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction
Anomaly freedom in Seiberg-Witten noncommutative gauge theories
We show that noncommutative gauge theories with arbitrary compact gauge group
defined by means of the Seiberg-Witten map have the same one-loop anomalies as
their commutative counterparts. This is done in two steps. By explicitly
calculating the \epsilon^{\m_1\m_2\m_3\m_4} part of the renormalized
effective action, we first find the would-be one-loop anomaly of the theory to
all orders in the noncommutativity parameter \theta^{\m\n}. And secondly we
isolate in the would-be anomaly radiative corrections which are not BRS
trivial. This gives as the only true anomaly occurring in the theory the
standard Bardeen anomaly of commutative spacetime, which is set to zero by the
usual anomaly cancellation condition.Comment: LaTeX 2e, no macros, no figures, 32 A4 page
Algebra Structures on Hom(C,L)
We consider the space of linear maps from a coassociative coalgebra C into a
Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry
properties of the induced bracket on Hom(C,L) fail to hold. We define the
concept of twisted domain (TD) algebras in order to recover the symmetries and
also construct a modified Chevalley-Eilenberg complex in order to define the
cohomology of such algebras
Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
Yang-Mills models with compact gauge group coupled to matter fields are
considered. The general tools developed in a companion paper are applied to
compute the local cohomology of the BRST differential modulo the exterior
spacetime derivative for all values of the ghost number, in the space of
polynomials in the fields, the ghosts, the antifields (=sources for the BRST
variations) and their derivatives. New solutions to the consistency conditions
depending non trivially on the antifields are exhibited. For a
semi-simple gauge group, however, these new solutions arise only at ghost
number two or higher. Thus at ghost number zero or one, the inclusion of the
antifields does not bring in new solutions to the consistency condition
besides the already known ones. The analysis does not use power
counting and is purely cohomological. It can be easily extended to more general
actions containing higher derivatives of the curvature, or Chern-Simons terms.Comment: 30 pages Latex file, ULB-TH-94/07, NIKHEF-H 94-1
Parent formulation at the Lagrangian level
The recently proposed first-order parent formalism at the level of equations
of motion is specialized to the case of Lagrangian systems. It is shown that
for diffeomorphism-invariant theories the parent formulation takes the form of
an AKSZ-type sigma model. The proposed formulation can be also seen as a
Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach.
We also discuss its possible interpretation as a multidimensional
generalization of the Hamiltonian BFV--BRST formalism. The general construction
is illustrated by examples of (parametrized) mechanics, relativistic particle,
Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected,
references adde
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