Perturbative Couplings of Vector Multiplets in $N=2$ Heterotic String Vacua

TL;DR

This paper investigates the structure of vector multiplet couplings in $N=2$ heterotic string vacua, analyzing both classical and quantum effects, with a focus on the constraints imposed by symmetries and the form of the prepotential.

Contribution

It provides a detailed analysis of the perturbative prepotential and its transformation properties in toroidal compactifications of six-dimensional $N=1$ vacua, highlighting the constraints from string symmetries.

Findings

Couplings are fixed at tree level by the theory's structure.

Loop corrections are highly constrained by discrete symmetries.

The transformation law of the prepotential is explicitly determined.

Abstract

We study the low-energy effective Lagrangian of $N=2$ heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional $N=1$ supersymmetric vacua.