arXiv subjects
Publications and source records attributed to A. Zaffaroni.
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry breaking, the approach, combined with the quantum action principle, leads to a rather simple proof to all orders.
We address the problem of constructing the family of (4,4) theories associated with the sigma-model on a parametrized family ${\cal M}_ζ$ of Asymptotically Locally Euclidean (ALE) manifolds. We rely on the ADE classification of these manifolds and on their construction as HyperKähler quotients, due to Kronheimer. So doing we are able to define the family of (4,4) theories corresponding to a ${\cal M}_ζ$ family of ALE manifolds as the deformation of a solvable orbifold ${\bf C}^2 \, / \, Γ$ conformal field-theory, $Γ$ being a Kleinian group. We discuss the relation among the algebraic structure underlying the topological and metric properties of self-dual 4-manifolds and the algebraic properties of non-rational (4,4)-theories admitting an infinite spectrum of primary fields. In particular, we identify the Hirzebruch signature $τ$ with the dimension of the local polynomial ring ${\cal R}=ø{{\bf C}[x,y,z]}{\partial W}$ associated with the ADE singularity, with the number of non-trivial conjugacy classes in the corresponding Kleinian group and with the number of short representations of the (4,4)-theory minus four.
We study the problem of string propagation in a general instanton background for the case of the complete heterotic superstring. We define the concept of generalized HyperK\" ahler manifolds and we relate it to (4,4) superconformal theories. We propose a generalized h-map construction that predicts a universal SU(6) symmetry for the modes of the string excitations moving in an instanton background. We also discuss the role of abstract $N$=4 moduli and, applying it to the particular limit case of the solvable SU(2) X R instanton found by Callan et al. we show that it admits deformations and corresponds to a point in a 16-dimensional moduli space. The geometrical characterization of the other spaces in the same moduli-space remains an outstanding problem.