String Amplitudes and N=2, d=4 Prepotential in Heterotic K3 x T^2 Compactifications

TL;DR

This paper computes one-loop gauge coupling corrections in heterotic string compactifications on K3 x T^2, relating string amplitude calculations to N=2 prepotential structures and special geometry.

Contribution

It provides explicit calculations of one-loop gauge couplings and uncovers relations between prepotential derivatives and world-sheet tau-integrals in T^2 compactifications.

Findings

Calculated one-loop corrections to gauge couplings.

Established relations between prepotential derivatives and string amplitudes.

Connected string amplitude results with N=2 special geometry equations.

Abstract

For the gauge couplings, which arise after toroidal compactification of six-dimensional heterotic N=1 string theories from the T^2 torus, we calculate their 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 tau-integrals which appear in various string amplitudes of any T^2-compactification.