Harmonicity in N = 4 supersymmetry and its quantum anomaly

The holomorphicity property of N = 1 superpotentials or of N = 2 F-terms involving vector multiplets is generalized to the case of N = 4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N = 4 Weyl superfield, computed by N = 4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings. ignatios.antoniadis@cern.ch On leave from CPHT (UMR CNRS 7644) Ecole Polytechnique, F-91128 Palaiseau stefan.hohenegger@cern.ch narain@ictp.trieste.it emeri.sokatchev@cern.ch UMR 5108 associée à l’Université de Savoie