, tous droits réservés. L'accès aux archives de la série « Recherche Coopérative sur Programme n o 25 » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/-297-aOOaNftLIZATIOH OF GAUGE THEORIES
, tous droits réservés. L'accès aux archives de la série « Recherche Coopérative sur Programme n o 25 » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/-243-RBNORMALIZATION OF THE ABELIAN HIGGS-KIBBLE MODEL
The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of "descent equations".
We classify 2-center extremal black hole charge configurations through duality-invariant homogeneous polynomials, which are the generalization of the unique invariant quartic polynomial for single-center black holes based on homogeneous symmetric cubic special Kähler geometries.A crucial role is played by an horizontal SL(p, R) symmetry group, which classifies invariants for p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants emerge. We provide the minimal set of independent invariants for the rank-3 N = 2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st 2 and rank-1 t 3 models; these models respectively exhibit seven, six and five independent invariants.We also derive the polynomial relations among these and other duality invariants. In particular, the symplectic product of two charge vectors is not independent from the quartic quintet in the t 3 model, but rather it satisfies a degree-16 relation, corresponding to a quartic equation for the square of the symplectic product itself.
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