355 research outputs found
Seiberg-Witten maps and anomalies in noncommutative Yang-Mills theories
A BRST-cohomological analysis of Seiberg-Witten maps and results on gauge
anomalies in noncommutative Yang-Mills theories with general gauge groups are
reviewed.Comment: 9 pages, talk at 9th Adriatic Meeting, Dubrovnik, Croatia, 4-14 Sept.
200
Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
Seiberg-Witten maps and a recently proposed construction of noncommutative
Yang-Mills theories (with matter fields) for arbitrary gauge groups are
reformulated so that their existence to all orders is manifest. The ambiguities
of the construction which originate from the freedom in the Seiberg-Witten map
are discussed with regard to the question whether they can lead to inequivalent
models, i.e., models not related by field redefinitions.Comment: 12 pages; references added, minor misprints correcte
Parent form for higher spin fields on anti-de Sitter space
We construct a first order parent field theory for free higher spin gauge
fields on constant curvature spaces. As in the previously considered flat case,
both Fronsdal's and Vasiliev's unfolded formulations can be reached by two
different straightforward reductions. The parent theory itself is formulated
using a higher dimensional embedding space and turns out to be geometrically
extremely transparent and free of the intricacies of both of its reductions.Comment: 39 pages, LaTeX; misprints corrected, references adde
An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
It is a general belief that the only possible way to consistently deform the
Pauli-Fierz action, changing also the gauge algebra, is general relativity.
Here we show that a different type of deformation exists in three dimensions if
one allows for PT non-invariant terms. The new gauge algebra is different from
that of diffeomorphisms. Furthermore, this deformation can be generalized to
the case of a collection of massless spin-two fields. In this case it describes
a consistent interaction among them.Comment: 21+1 pages. Minor corrections and reference adde
Scale Transformations on the Noncommutative Plane and the Seiberg-Witten Map
We write down three kinds of scale transformations {\tt i-iii)} on the
noncommutative plane. {\tt i)} is the analogue of standard dilations on the
plane, {\tt ii)} is a re-scaling of the noncommutative parameter , and
{\tt iii)} is a combination of the previous two, whereby the defining relations
for the noncommutative plane are preserved. The action of the three
transformations is defined on gauge fields evaluated at fixed coordinates and
.
The transformations are obtained only up to terms which transform covariantly
under gauge transformations. We give possible constraints on these terms. We
show how the transformations {\tt i)} and {\tt ii)} depend on the choice of
star product, and show the relation of {\tt ii)} to Seiberg-Witten
transformations. Because {\tt iii)} preserves the fundamental commutation
relations it is a symmetry of the algebra. One has the possibility of
implementing it as a symmetry of the dynamics, as well, in noncommutative field
theories where is not fixed.Comment: 20 page
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
Self-interactions in a topological BF-type model in D=5
All consistent interactions in five spacetime dimensions that can be added to
a free BF-type model involving one scalar field, two types of one-forms, two
sorts of two-forms, and one three-form are investigated by means of deforming
the solution to the master equation with the help of specific cohomological
techniques. The couplings are obtained on the grounds of smoothness, locality,
(background) Lorentz invariance, Poincar\'{e} invariance, and the preservation
of the number of derivatives on each field.Comment: LaTeX, 57 pages, final version, matching the published pape
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
On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories
We apply the BV formalism to non-commutative field theories, introduce BRST
symmetry, and gauge-fix the models. Interestingly, we find that treating the
full gauge symmetry in non-commutative models can lead to reducible gauge
algebras. As one example we apply the formalism to the Connes-Lott two-point
model. Finally, we offer a derivation of a superversion of the
Harish-Chandra-Itzykson-Zuber integral.Comment: 20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about
Harish-Chandra-Itzykson-Zuber integrals. v4: Added Reference
Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)
The main BRST cohomological properties of a free, massless tensor field that
transforms in an irreducible representation of GL(D,R), corresponding to a
rectangular, two-column Young diagram with k>2 rows are studied in detail. In
particular, it is shown that any non-trivial co-cycle from the local BRST
cohomology group H(s|d) can be taken to stop either at antighost number (k+1)
or k, its last component belonging to the cohomology of the exterior
longitudinal derivative H(gamma) and containing non-trivial elements from the
(invariant) characteristic cohomology H^{inv}(delta|d).Comment: Latex, 50 pages, uses amssym
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