String amplitudes and N = 2, d = 4 prepotential in heterotic K3 × T2 compactifications Original Research Article

For the gauge couplings that arise after toroidal compactification of six-dimensional heterotic N = 1 string theories from the T2 torus we calculate the one-loop corrections. This is performed by considering string amplitudes involving two gauge fields and moduli fields. We compare our results with the equations following from N = 2 special geometry and the underlying prepotential of the theory. Moreover, we find relations between derivatives of the N = 2, d = 4 prepotential and world-sheet τ-integrals which appear in various string amplitudes of any T2 compactification.