The master equation for the prepotential Original Research Article

The perturbative prepotential and the Kähler metric of the vector multiplets of the N = 2 effective low-energy heterotic strings is calculated directly in N = 1 six-dimensional toroidal compactifications of the heterotic string vacua. This method provides the solution for the one-loop correction to the N = 2 vector multiplet prepotential for compactifications of the heterotic string for any rank-3 and rank-4 models, as well for compactifications on K3 × T2. In addition, we complete previous calculations, derived from string amplitudes, by deriving the differential equation for the third derivative of the prepotential with respect of the usual complex structure U moduli of the T2 torus. Moreover, we calculate the one-loop prepotential, using its modular properties, for N = 2 compactifications of the heterotic string exhibiting modular groups similar with those appearing in N = 2 sectors of N = 1 orbifolds based on non-decomposable torus lattices and on N = 2 supersymmetric Yang-Mills.