876 research outputs found
Supersymmetry algebra cohomology III: Primitive elements in four and five dimensions
The primitive elements of the supersymmetry algebra cohomology as defined in
a previous paper are computed for standard supersymmetry algebras in four and
five dimensions, for all signatures of the metric and any number of
supersymmetries.Comment: v2: D=4 analysis simplified, D=5 analysis added, refs. added, typos
corrected, 32 page
Symmetries of the Chern-Simons Theory in the Axial Gauge, Manifold with Boundary
The field equations of the Chern-Simons theory quantized in the axial gauge
are shown to be completely determined by supersymmetry Ward identities which
express the invariance of the theory under the topological supersymmetry of
Delduc, Gieres and Sorella together with the usual Slavnov identity without
requiring any action principle.Comment: 8 pages LaTeX, report UGVA-DPT 1994/01-84
Supersymmetry algebra cohomology I: Definition and general structure
The paper concerns standard supersymmetry algebras in diverse dimensions,
involving bosonic translational generators and fermionic supersymmetry
generators. A cohomology related to these supersymmetry algebras, termed
supersymmetry algebra cohomology, and corresponding "primitive elements" are
defined by means of a BRST-type coboundary operator. A method to systematically
compute this cohomology is outlined and illustrated by simple examples.Comment: v5: matches published version; 3 refs., section 5.5 and
remarks/comments in sections 1, 2.8, 3 and 7 added; minor editorial
improvements and change of titl
Five-Dimensional BF Theory and Four-Dimensional Current Algebra
We consider the relation between the five-dimensional BF model and a
four-dimensional local current algebra from the point of view of perturbative
local quantum field theory. We use an axial gauge fixing procedure and show
that it allows for a well defined theory which actually can be solved exactly.Comment: 15 pages LaTeX file +3 Figures in TexDraw (available from hep-th)
LATEX-compatibility Bug fixe
Kodaira-Spencer deformation of complex structures and Lagrangian field theory
In complete analogy with the Beltrami parametrization of complex structures
on a (compact) Riemann surface, we use in this paper the Kodaira-Spencer
deformation theory of complex structures on a (compact) complex manifold of
higher dimension. According to the Newlander-Nirenberg theorem, a smooth change
of local complex coordinates can be implemented with respect to an integrable
complex structure parametrized by a Beltrami differential. The question of
constructing a local field theory on a complex compact manifold is addressed
and the action of smooth diffeomorphisms is studied in the BRS algebraic
approach. The BRS cohomology for the diffeomorphisms gives rise to generalized
Gel'fand-Fuchs cocycles provided that the Kodaira-Spencer integrability
condition is satisfied. The diffeomorphism anomaly is computed and turns out to
be holomorphically split as in the bidimensional Lagrangian conformal models.
Moreover, its algebraic structure is much more complicated than the one
proposed in a quite recent paper hep-th/9606082 (Nucl. Phys. B484 (1997) 196).Comment: LaTeX, 30 pages, no figure. Submitted to Journ. Math. Phy
No radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences
The issue intensively claimed in the literature on the generation of a
CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections
owing to a CPT violating interaction -- the axial coupling of fermions with a
constant vector field b_\m -- is mistaken. The presence of massless gauge
field triggers IR divergences that might show up from the UV subtractions,
therefore, so as to deal with the (actual physical) IR divergences, the
Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL
renormalization method, has to be adopted. The proof on the non generation of
such a Chern-Simons-like term is done, independent of any kind of
regularization scheme, at all orders in perturbation theory.Comment: In honor of Prof. Manfred Schweda (1939-2017). Work presented at the
XXXVIII National Meeting on Particle Physics and Fields, September 18-22,
2017 - Passa Quatro - Minas Gerais - Brazil. Reference [46] correcte
On Consistency Of Noncommutative Chern-Simons Theory
We consider the noncommutative extension of Chern-Simons theory. We show the
the theory can be fully expanded in power series of the noncommutative
parameter theta and that no non-analytical sector exists. The theory appears to
be unstable under radiative corrections, but we show that the infinite set of
instabilities, to all orders in \hbar and in theta, is confined to a BRS exact
cocycle. We show also that the theory is anomaly free. The quantum theory
cannot be written in terms of the Groenewald-Moyal star product, and hence
doubts arise on the interpretation of the noncommutative nature of the
underlying spacetime. Nonetheless, the deformed theory is well defined as a
quantum field theory, and the beta function of the Chern-Simons coupling
constant vanishes, as in the ordinary Chern-Simons theory.Comment: 17 page
N=2 Super Yang Mills Action and BRST Cohomology
The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in
the framework of Algebraic Renormalization. In particular, N=2 supersymmetric
descent equations are derived from the cohomological analysis of linearized
Slavnov-Taylor operator \B. It is then shown that both off- and on-shell N=2
super Yang-Mills actions are related to a lower-dimensional gauge invariant
field polynomial Tr\f^2 by solving these descent equations. Moreover, it is
found that these off- and on-shell solutions differ only by a \B-exact term,
which can be interprated as a consequence of the fact that the cohomology of
both cases are the same.Comment: Latex, 1+13 page
Remarks on Existence of Proper Action for Reducible Gauge Theories
In the field-antifield formalism, we review existence and uniqueness proofs
for the proper action in the reducible case. We give two new existence proofs
based on two resolution degrees called "reduced antifield number" and "shifted
antifield number", respectively. In particular, we show that for every choice
of gauge generators and their higher stage counterparts, there exists a proper
action that implements them at the quadratic order in the auxiliary variables.Comment: 37 pages, LaTeX. v2,v3: Minor corrections. v4: Added reference. To
appear in IJMP
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