862 research outputs found
Topological Gravity versus Supergravity on Manifolds with Special Holonomy
We construct a topological theory for euclidean gravity in four dimensions,
by enforcing self-duality conditions on the spin connection. The corresponding
topological symmetry is associated to the SU(2) X diffeomorphism X U(1)
invariance. The action of this theory is that of d=4, N=2 supergravity, up to a
twist. The topological field theory is SU(2) invariant, but the full SO(4)
invariance is recovered after untwist. This suggest that the topological
gravity is relevant for manifolds with special holonomy. The situation is
comparable to that of the topological Yang-Mills theory in eight dimensions,
for which the SO(8) invariance is broken down to Spin(7), but is recovered
after untwisting the topological theory.Comment: LateX file, 19 page
Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity
In a previous work, it was shown that the 8-dimensional topological quantum
field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1
D = 8 supergravity. It is shown here that, the combination of this TQFT with
that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated
dimensional reduction of N = 1 D = 11 supergravity. Our construction holds for
8-dimensional manifolds with Spin(7) \subset SO(8) holonomy. We suggest that
the origin of local Poincare supersymmetry is the gravitational topological
symmetry. We indicate a mechanism for the lift of the TQFT in higher
dimensions, which generates Chern-Simons couplings.Comment: one section has been adde
Geometrical Interpretation of BRST Symmetry in Topological Yang-Mills-Higgs Theory
We study topological Yang-Mills-Higgs theories in two and three dimensions
and topological Yang-Mills theory in four dimensions in a unified framework of
superconnections. In this framework, we first show that a classical action of
topological Yang-Mills type can provide all three classical actions of these
theories via appropriate projections. Then we obtain the BRST and anti-BRST
transformation rules encompassing these three topological theories from an
extended definition of curvature and a geometrical requirement of Bianchi
identity. This is an extension of Perry and Teo's work in the topological
Yang-Mills case. Finally, comparing this result with our previous treatment in
which we used the ``modified horizontality condition", we provide a meaning of
Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST
symmetry in a geometrical setting.Comment: 16 pages, LaTeX fil
Gauge Group TQFT and Improved Perturbative Yang-Mills Theory
We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills
theories as the definition of a topological quantum field theory for gauge
group elements depending on a background connection. This has the advantage of
relating topological gauge-fixing ambiguities to the global breaking of a
supersymmetry. The global zero modes of the Faddeev-Popov ghosts are handled in
the context of an equivariant cohomology without breaking translational
invariance. The gauge-fixing involves constant fields which play the role of
moduli and modify the behavior of Green functions at subasymptotic scales. At
the one loop level physical implications from these power corrections are gauge
invariant.Comment: 28 pages, uuencoded and compressed tar-file, LATEX+4 PS-figures, uses
psfig.sty. New appendix and some clarifying modifications, references adde
One-dimensional structures behind twisted and untwisted superYang-Mills theory
We give a one-dimensional interpretation of the four-dimensional twisted N=1
superYang-Mills theory on a Kaehler manifold by performing an appropriate
dimensional reduction. We prove the existence of a 6-generator superalgebra,
which does not possess any invariant Lagrangian but contains two different
subalgebras that determine the twisted and untwisted formulations of the N=1
superYang-Mills theory.Comment: 12 pages. Final version to appear in Lett. Math. Phys. with improved
notation and misprints correcte
Extended BRST invariance in topological Yang Mills theory revisited
Extended BRST invariance (BRST plus anti-BRST invariances) provides in
principle a natural way of introducing the complete gauge fixing structure
associated to a gauge field theory in the minimum representation of the
algebra. However, as it happens in topological Yang Mills theory, not all gauge
fixings can be obtained from a symmetrical extended BRST algebra, where
antighosts belong to the same representation of the Lorentz group of the
corresponding ghosts. We show here that, at non interacting level, a simple
field redefinition makes it possible to start with an extended BRST algebra
with symmetric ghost antighost spectrum and arrive at the gauge fixing action
of topological Yang Mills theory.Comment: Interaction terms heve been included in all the calculations. Two
references added. Version to be published in Phys. Rev. D. 7 pages, Latex, no
figure
Proposal of a topological M(atrix) theory
Keeping in mind the several models of M(atrix) theory we attempt to
understand the possible structure of the topological M(atrix) theory
``underlying'' these approaches. In particular we are motivated by the issue
about the nature of the structure of the vacuum of the topological M(atrix)
theory and how this could be related to the vacuum of the electroweak theory.
In doing so we are led to a simple topological matrix model. Moreover it is
intuitively expected from the current understanding that the noncommutative
nature of ``spacetime'' and background independence should lead to a
topological Model. The main purpose of this note is to propose a simple
topological Matrix Model which bears relation to F and M theories. Suggestions
on the origin of the chemical potential term appearing in the matrix models are
given.Comment: 14 pages revte
Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region
We prove the renormalizability of a quark-gluon model with a soft breaking of
the BRST symmetry, which accounts for the modification of the large distance
behavior of the quark and gluon correlation functions. The proof is valid to
all orders of perturbation theory, by making use of softly broken Ward
identities.Comment: 20 pages, no figures. Preprint number added in v2
Superfield algorithm for higher order gauge field theories
We propose an algorithm for the construction of higher order gauge field
theories from a superfield formulation within the Batalin-Vilkovisky formalism.
This is a generalization of the superfield algorithm recently considered by
Batalin and Marnelius. This generalization seems to allow for non-topological
gauge field theories as well as alternative representations of topological
ones. A five dimensional non-abelian Chern-Simons theory and a topological
Yang-Mills theory are treated as examples.Comment: 17 pages in LaTeX, improved text, published versio
BRST Formulation of 4-Monopoles
A supersymmetric gauge invariant action is constructed over any 4-dimensional
Riemannian manifold describing Witten's theory of 4-monopoles. The topological
supersymmetric algebra closes off-shell. The multiplets include the auxiliary
fields and the Wess-Zumino fields in an unusual way, arising naturally from
BRST gauge fixing. A new canonical approach over Riemann manifolds is followed,
using a Morse function as an euclidean time and taking into account the BRST
boundary conditions that come from the BFV formulation. This allows a
construction of the effective action starting from gauge principles.Comment: 18 pages, Amste
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