86 research outputs found
Diffeomorphism Cohomology in Beltrami Parametrization II : The 1-Forms
We study the 1-form diffeomorphism cohomologies within a local conformal
Lagrangian Field Theory model built on a two dimensional Riemann surface with
no boundary. We consider the case of scalar matter fields and the complex
structure is parametrized by Beltrami differential. The analysis is first
performed at the Classical level, and then we improve the quantum extension,
introducing the current in the Lagrangian dynamics, coupled to external source
fields. We show that the anomalies which spoil the current conservations take
origin from the holomorphy region of the external fields, and only the
differential spin 1 and 2 currents (as well their c.c) could be anomalous.Comment: 39 pages,CPT-94/P.3072,LaTe
W-(infinity)-algebras in n complex dimensions and Kodaira-Spencer deformations : a symplectic approach
It is shown that the notion of W_\infty-algebra originally carried out over a
(compact) Riemann surface can be extended to n complex dimensional (compact)
manifolds within a symplectic geometrical setup. The relationships with the
Kodaira-Spencer deformation theory of complex structures are discussed.
Subsequently, some field theoretical aspects at the classical level are briefly
underlined.Comment: LaTex, 20 pages, no figures, version to be published in Journ. Math.
Phy
The role of complex structures in w-symmetry
In a symplectic framework, the infinitesimal action of symplectomorphisms
together with suitable reparametrizations of the two dimensional complex base
space generate some type of W-algebras. It turns out that complex structures
parametrized by Beltrami differentials play an important role in this context.
The construction parallels very closely two dimensional Lagrangian conformal
models where Beltrami differentials are fundamental.Comment: LaTex, 34 pages, no figures, to be published in Nucl. Phys.
Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a
complex scalar field over a Riemann surface is presented in the paper under the
name of large diffeomorphisms. After an heuristic approach, we show how a
linear truncation in the Taylor expansion can generate an algebra of symmetry
characterized by some structure functions. Such a linear truncation is
explicitly realized by introducing the notion of Forsyth frame over the Riemann
surface with the help of a conformally covariant algebraic differential
equation. The large chiral diffeomorphism action is then implemented through a
B.R.S. formulation (for a given order of truncation) leading to a more
algebraic set up. In this context the ghost fields behave as holomorphically
covariant jets. Subsequently, the link with the so called W-algebras is made
explicit once the ghost parameters are turned from jets into tensorial ghost
ones. We give a general solution with the help of the structure functions
pertaining to all the possible truncations lower or equal to the given order.
This provides another contribution to the relationship between KdV flows and
W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys.
Work partly supported by Region PACA and INF
SU(N) chiral gauge theories on the lattice
We extend the construction of lattice chiral gauge theories based on
non-perturbative gauge fixing to the non-abelian case. A key ingredient is that
fermion doublers can be avoided at a novel type of critical point which is only
accessible through gauge fixing, as we have shown before in the abelian case.
The new ingredient allowing us to deal with the non-abelian case as well is the
use of equivariant gauge fixing, which handles Gribov copies correctly, and
avoids Neuberger's no-go theorem. We use this method in order to gauge fix the
non-abelian group (which we will take to be SU(N)) down to its maximal abelian
subgroup. Obtaining an undoubled, chiral fermion content requires us to
gauge-fix also the remaining abelian gauge symmetry. This modifies the
equivariant BRST identities, but their use in proving unitarity remains intact,
as we show in perturbation theory. On the lattice, equivariant BRST symmetry as
well as the abelian gauge invariance are broken, and a judiciously chosen
irrelevant term must be added to the lattice gauge-fixing action in order to
have access to the desired critical point in the phase diagram. We argue that
gauge invariance is restored in the continuum limit by adjusting a finite
number of counter terms. We emphasize that weak-coupling perturbation theory
applies at the critical point which defines the continuum limit of our lattice
chiral gauge theory.Comment: 39 pages, 3 figures, A number of clarifications adde
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
Landau gauge within the Gribov horizon
We consider a model which effectively restricts the functional integral of
Yang--Mills theories to the fundamental modular region. Using algebraic
arguments, we prove that this theory has the same divergences as ordinary Yang
Mills theory in the Landau gauge and that it is unitary. The restriction of the
functional integral is interpreted as a kind of spontaneous breakdown of the
symmetry.Comment: 17 pages, NYU-TH-93/10/0
Primary currents and Riemannian geometry in W-algebras
It is proved that general consistency requirements of stability under complex
analytic change of charts show that primary currents in finite chiral
W-algebras are described in terms of pure gravitational variables.Comment: LaTex, 18 pages, no figures, version to appear in Nucl. Phys.
Yang-Mills gauge anomalies in the presence of gravity with torsion
The BRST transformations for the Yang-Mills gauge fields in the presence of
gravity with torsion are discussed by using the so-called Maurer-Cartan
horizontality conditions. With the help of an operator \d which allows to
decompose the exterior spacetime derivative as a BRST commutator we solve the
Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms
and gauge anomalies.Comment: 24 pages, report REF. TUW 94-1
Induced quantum gravity on a Riemann Surface
Induced quantum gravity dynamics built over a Riemann surface is studied in
arbitrary dimension. Local coordinates on the target space are given by means
of the Laguerre-Forsyth construction. A simple model is proposed and
pertubatively quantized. In doing so, the classical W-symmetry turns out to be
preserved on-shell at any order of the perturbative expansion. As a
main result, due to quantum corrections, the target coordinates acquire a
non-trivial character.Comment: LaTex, 32 pages, no figures, submitted to Int. J. Mod. Phys.
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