65 research outputs found
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
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
Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
If the Wilsonian renormalization group (RG) is formulated with a cutoff that
breaks gauge invariance, then gauge invariance may be recovered only once the
cutoff is removed and only once a set of effective Ward identities is imposed.
We show that an effective Quantum Action Principle can be formulated in
perturbation theory which enables the effective Ward identities to be solved
order by order, even if the theory requires non-vanishing subtraction points.
The difficulties encountered with non-perturbative approximations are briefly
discussed.Comment: 11 pages, latex, no figures, one reference added, version to be
published on Phys. Lett.
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.
W-algebras from symplectomorphisms
It is shown how -algebras emerge from very peculiar canonical
transformations with respect to the canonical symplectic structure on a compact
Riemann surface. The action of smooth diffeomorphisms of the cotangent bundle
on suitable generating functions is written in the BRS framework while a
-symmetry is exhibited. Subsequently, the complex structure of the symmetry
spaces is studied and the related BRS properties are discussed. The specific
example of the so-called -algebra is treated in relation to some other
different approaches.Comment: LaTex, 25 pages, no figures, to appear in Journ. Math. Phy
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
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
Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories
A new way of solving the descent equations corresponding to the Wess-Zumino
consistency conditions is presented. The method relies on the introduction of
an operator which allows to decompose the exterior space-time
derivative as a commutator. The case of the Yang-Mills theories is
treated in detail.Comment: 16 pages, UGVA-DPT 1992/08-781 to appear in Comm. Math. Phy
The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
We complete our study of non-Abelian gauge theories in the framework of
Epstein-Glaser approach to renormalization theory including in the model an
arbitrary number of Dirac Fermions. We consider the consistency of the model up
to the third order of the perturbation theory. In the second order we obtain
pure group theoretical relations expressing a representation property of the
numerical coefficients appearing in the left and right handed components of the
interaction Lagrangian. In the third order of the perturbation theory we obtain
the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate
The Nielsen Identities of the SM and the definition of mass
In a generic gauge theory the gauge parameter dependence of individual Green
functions is controlled by the Nielsen identities, which originate from an
enlarged BRST symmetry. We give a practical introduction to the Nielsen
identities of the Standard Model (SM) and to their renormalization and
illustrate the power of this elegant formalism in the case of the problem of
the definition of mass.We prove to all orders in perturbation theory the
gauge-independence of the complex pole of the propagator for all physical
fields of the SM, in the most general case with mixing and CP violation. At the
amplitude level, the formalism provides an intuitive and general understanding
of the gauge recombinations which makes it particularly useful at higher
orders. We also include in an appendix the explicit expressions for the
fermionic two-point functions in a generic R_\xi gauge.Comment: 28 pages, LaTeX2e, 4 Postscript Figures, final version to appear on
PRD, extensive revision
- …