179 research outputs found
Faddeev-Jackiw Analysis of Topological Mass Generating Action
We analyze the gauge symmetry of a topological mass generating action in four
dimensions which contains both a vector and a second rank antisymmetric tensor
fields. In the Abelian case, this system induces an effective mass for the
vector gauge field via a topological coupling in the presence of a
kinetic term for the antisymmetric tensor field , while maintaining a gauge
symmetry. On the other hand, for the non-Abelian case the field does not
have a gauge symmetry unless an auxiliary vector field is introduced to the
system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and
show how the auxiliary vector field enhances the symmetry. At the same time
this enhanced gauge symmetry becomes reducible. We also show this phenomenon in
this analysis.Comment: 20 pages, REVTe
Algebraic structure of gravity in Ashtekar variables
The BRST transformations for gravity in Ashtekar variables are obtained by
using the Maurer-Cartan horizontality conditions. The BRST cohomology in
Ashtekar variables is calculated with the help of an operator
introduced by S.P. Sorella, which allows to decompose the exterior derivative
as a BRST commutator. This BRST cohomology leads to the differential invariants
for four-dimensional manifolds.Comment: 19 pages, report REF. TUW 94-1
Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio
Semi-infinite cohomology of W-algebras
We generalize some of the standard homological techniques to \cW-algebras,
and compute the semi-infinite cohomology of the \cW_3 algebra on a variety of
modules. These computations provide physical states in \cW_3 gravity coupled
to \cW_3 minimal models and to two free scalar fields.Comment: 15 page
On the infrared behaviour of Gluons and Ghosts in Ghost-Antighost symmetric gauges
To investigate the possibility of a ghost-antighost condensate the coupled
Dyson--Schwinger equations for the gluon and ghost propagators in Yang--Mills
theories are derived in general covariant gauges, including ghost-antighost
symmetric gauges. The infrared behaviour of these two-point functions is
studied in a bare-vertex truncation scheme which has proven to be successful in
Landau gauge. In all linear covariant gauges the same infrared behaviour as in
Landau gauge is found: The gluon propagator is infrared suppressed whereas the
ghost propagator is infrared enhanced. This infrared singular behaviour
provides indication against a ghost-antighost condensate. In the
ghost-antighost symmetric gauges we find that the infrared behaviour of the
gluon and ghost propagators cannot be determined when replacing all dressed
vertices by bare ones. The question of a BRST invariant dimension two
condensate remains to be further studied.Comment: 34 pages, 6 figures, Version to be published in Phys. Rev.
Free Abelian 2-Form Gauge Theory: BRST Approach
We discuss various symmetry properties of the Lagrangian density of a four (3
+ 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge
theory is endowed with a Curci-Ferrari type condition which happens to be a key
signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the
above condition that the nilpotent BRST and anti-BRST symmetries of the theory
are found to be absolutely anticommuting in nature. For our present 2-form
gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry
properties of the Lagrangian densities and derive the corresponding conserved
charges. The algebraic structure, obeyed by the above conserved charges, is
deduced and the constraint analysis is performed with the help of the
physicality criteria where the conserved and nilpotent (anti-)BRST charges play
completely independent roles. These physicality conditions lead to the
derivation of the above Curci-Ferrari type restriction, within the framework of
BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc
On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
In the covariant description of confinement, one expects the ghost
correlations to be infrared enhanced. Assuming ghost dominance, the long-range
behavior of gluon and ghost correlations in Landau gauge QCD is determined by
one exponent kappa. The gluon propagator is infrared finite (vanishing) for
kappa =1/2 (kappa > 1/2) which is still under debate. Here, we study critical
exponent and coupling for the infrared conformal behavior from the asymptotic
form of the solutions to the Dyson-Schwinger equations in an ultraviolet finite
expansion scheme. The value for kappa is directly related to the ghost-gluon
vertex. Assuming that it is regular in the infrared, one obtains kappa = 0.595.
This value maximizes the critical coupling alpha_c(kappa), yielding alpha_c^max
= (4 Pi/Nc) 0.709 approx. 2.97 for Nc=3. For larger kappa the vertex acquires
an infrared singularity in the gluon momentum, smaller ones imply infrared
singular ghost legs. Variations in alpha_c remain within 5% from kappa = 0.5 to
0.7. Above this range, alpha_c decreases more rapidly with alpha_c -> 0 as
kappa -> 1 which sets the upper bound on kappa.Comment: 22 Pages, 10 Figures, LaTeX2e, revtex4, some notes and references
added in response to communication
Symmetries of topological field theories in the BV-framework
Topological field theories of Schwarz-type generally admit symmetries whose
algebra does not close off-shell, e.g. the basic symmetries of BF models or
vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this
symmetry being at the origin of the perturbative finiteness of the theory). We
present a detailed discussion of all these symmetries within the algebraic
approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general
algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page
Generalized Geometry and M theory
We reformulate the Hamiltonian form of bosonic eleven dimensional
supergravity in terms of an object that unifies the three-form and the metric.
For the case of four spatial dimensions, the duality group is manifest and the
metric and C-field are on an equal footing even though no dimensional reduction
is required for our results to hold. One may also describe our results using
the generalized geometry that emerges from membrane duality. The relationship
between the twisted Courant algebra and the gauge symmetries of eleven
dimensional supergravity are described in detail.Comment: 29 pages of Latex, v2 References added, typos fixed, v3 corrected
kinetic term and references adde
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