Giuseppe Bandelloni

Nonpolynomial Yang--Mills local cohomology

The spectral sequence method is used to find the nonintegrated function cohomology of the BRS Yang–Mills operator in the space of the analytic (a priori nonpolynomial) functions in space‐time dimensions.

{Yang-Mills} Cohomology in Four-dimensions

The local polynomial cohomology space of the Yang–Mills BRS operator in four dimensions is computed. In order to simplify the analysis, without omitting the physically interesting cases, the investigation is limited to polynomials whose Fadeev–Popov charge and UV naive dimensions have upper bounds. Furthermore the results are used to compute, a la Stora, the local functional Yang–Mills anomalies, from which the uniqueness of the Adler–Bardeen–Jackiw anomaly follows.

Diffeomorphism cohomology in Beltrami parametrization. II. The 1‐forms

The 1‐form diffeomorphism cohomologies within a local conformal Lagrangian field theory model built on a two dimensional Riemann surface with no boundary is studied. The case of scalar matter fields is considered 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. It is shown that the anomalies which spoil the current conservations take origin from the holomorphic region of the external fields, and only the differential spin 1 and 2 currents (as well as their c.c) could be anomalous.

Kodaira-Spencer deformation of complex structures and Lagrangian field theory

Similar to the Beltrami parametrization of complex structures on a (compact) Riemann surface, we use in this paper the Kodaira-Spencer deformation theory of complex structures on a (compact) complex manifold of higher dimension. According to the Newlander-Nirenberg theorem, a smooth change of local complex coordinates is implemented with respect to an integrable complex structure parametrize by a Beltrami differential. The question of constructing a local field theory on a complex compact manifold is addressed and the action of smooth diffeomorphisms is studied in the BRS algebraic approach. The BRS cohomology for the diffeomorphisms gives generalized Gel’fand-Fuchs cocycles provided that the Kodaira-Spencer integrability condition is satisfied. The diffeomorphism anomaly is computed and turns out to be holomorphically split as in the bidimensional Lagrangian conformal models. Moreover, its algebraic structure is much more complicated than the one proposed in a recent paper [Losev et al. Nuc. Phys. B 484, 196 (1997)].

Gravitational anomalies in two dimensions: A cohomological approach

The spectral sequences method is employed to study the cohomology space of the Becchi–Rouet–Stora (BRS) operator, which describes the general coordinate transformations in a two‐dimensional polynomial Lagrangian field theory. A pure external gravitational model is considered. In the Fadeev–Popov charge‐one sector, two classes of elements are found: the first represents the ordinary trace anomalies, in the second the presence of the anomalies recently calculated by Bardeen and Zumino are pointed out.

NONLINEAR EXTENSIONS OF THE REPARAMETRIZATION ALGEBRA: ALGEBRAIC CONSTRUCTION, INVARIANTS AND ANOMALIES

We perform a class of nonlinear extensions of the reparametrization algebra at arbitrary dimensions. Our extended algebras reproduce in the one-dimensional limit the well-known -ones. We point out the existence of a family of reparametrization invariant functions for which this property is untouched by the extension procedure. This allows to calculate the improvement of the gravitational anomaly within the extended symmetry.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

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 Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. 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 al...

Renormalization of gauge coset models

The renormalization of a four‐dimensional pure Yang–Mills model built on a compact homogeneous coset space is studied. The possible anomalies are explicitly derived.

Gauge theories on loop groups

A Becchi–Rouet–Stora (BRS) operator is built whose nilpotency is fixed not only by the group algebra relations, but also by the algebra extensions consistency conditions. It is applied on the renormalization of a simple Kac–Moody inspired gauge model.