Harmonicity in N=4 supersymmetry and its quantum anomaly

Abstract

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.

36 pages

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• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Borcherds Algebras and N=4 Topological Amplitudes
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Supersymmetry Constraints and String Theory on K3
• Probing the Moduli Dependence of Refined Topological Amplitudes
• A New Class of N=2 Topological Amplitudes
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation
• N=4 BPS black holes and octonionic twistors
• Obstructions and lines of marginal stability from the world-sheet
• N=4 Topological Amplitudes and Black Hole Entropy
• SU(4) harmonic superspace and supersymmetric gauge theory