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 $\hbar$ 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 $W$-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 $W$-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 $W_3$-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 $s$ modulo the exterior spacetime derivative $d$ 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 $sa+db=0$ 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 $sa+db=0$ 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 $\delta$ which allows to decompose the exterior space-time derivative $d$ as a $BRS$ 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