Raymond Stora

Gravitational anomalies of the Adler-Bardeen type

Abstract Gravitational anomalies of the Adler-Bardeen type are defined and studied by means of the usual Slavnov algebra, adapted to the case of an even-dimensional “space-time” maniford.

Renormalization of massless Feynman amplitudes in configuration space

A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.

Generalized Born--Infeld Actions and Projective Cubic Curves

We investigate U(1) n supersymmetric Born–Infeld Lagrangians with a second non–linearly realized supersymmetry. The resulting non–linear structure is more complex than the square root present in the standard Born–Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties.

On holomorphic factorization for free conformal fields

Abstract The holomorphic factorization theorem proved by the authors [Phys. Lett. B 262 (1991) 25], is extended to the case of free fields which are sections of an arbitrary holomorphic vector bundle over a compact Riemann surface without boundary.

Dirac and Weyl fermions coupled to two-dimensional surfaces: Determinants

Abstract The Dirac and Weyl fermion determinants are evaluated following the method indicated by Polyakov, Wiegmann and Witten, in the case of fermions coupled to two-dimensional surfaces embedded in the case of fermions coupled to two-dimensional surfaces embedded in R d .

RENORMALIZED PERTURBATION THEORY: A MISSING CHAPTER

Renormalized perturbation theory a la BPHZ can be founded on causality as analyzed by Epstein and Glaser in the seventies. Here, we list and discuss a number of additional constraints of algebraic character some of which have to be considered as parts of the core of the BPHZ framework.

The Wess Zumino consistency condition: a paradigm in renormalized perturbation theory†

Talk given at Symposium in Honor of Julius Wess on the Occasion of his 70th Birthday, 10-11 January 2005 at Max Planck Institute for Physics (Werner Heisenberg Institut) Fohringer Ring 6 - D-80805 MUENCHEN

EXERCISES IN EQUIVARIANT COHOMOLOGY

Equivariant cohomology [1]–[5] is at the core of the geometrical interpretation of the topological -more precisely, cohomological- field theories proposed by E. Witten in 1988 [6, 7]. The corresponding mathematical equipment also sheds some light on the gauge fixing procedure [8] familiar in the Lagrangian formulation of gauge theories.

The Role of Locality in String Quantization

Whereas free string quantization is by now part of the common knowledge, it still calls for some comments : it is a gauge theory, for the gauge group “Diff x Weyl” ; gauge fixing has then to be performed according to the Faddeev Popov procedure and the ensueing Slavnov symmetry can be found, given local gauge functions. It is customary to work in a Landau type conformal gauge and furthermore to eliminate the Weyl ghost and antighost as well as the multiplier field so that only a pair of diffeomorphism ghost and antighost are left over, besides the string field.

Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly

Configuration (x-)space renormalization of Euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group.