We consider the N = 4 supersymmetric Yang-Mills theory in four dimensions. We compute the one-loop contributions to the effective action with five external vector fields and compare them with corresponding results in open superstring theory. Our calculation determines the structure of the F 5 terms that appear in the nonabelian generalization of the Born Infeld action. The trace operation on the gauge group indices receives contributions from the symmetric as well as the antisymmetric part. We find that in order to study corrections to the symmetrized trace prescription one has to consistently take into account derivative contributions not only with antisymmetrized products ∇ [µ ∇ ν] but also with symmetrized ones ∇ (µ ∇ ν) .

We compute in superspace the one-loop beta-function for the nonlinear sigmamodel defined in terms of the nonminimal scalar multiplet. The recently proposed quantization of this complex linear superfield, viewed as the field strength of an unconstrained gauge spinor superfield, allows to handle efficiently the infinite tower of ghosts via the Batalin-Vilkovisky formalism. We find that the classical duality of the nonminimal scalar and chiral multiplets is maintained at the quantum one-loop level. † Onderzoeksdirecteur FWO, Belgium

IFUM-522-FT

We study the quantum integrability of nonsimply-laced affine Toda theories defined on the half-plane and explicitly construct the first nontrivial higher-spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the "bulk" current plays a relevant role for the quantum boundary conservation.

We study renormalizable nonlinear σ-models in two dimensions with N = 2 supersymmetry described in superspace in terms of chiral and complex linear superfields. The geometrical structure of the underlying manifold is investigated and the one-loop divergent contribution to the effective action is computed. The condition of vanishing β-function allows to identify a class of models which satisfy this requirement and possess N = 4 supersymmetry.