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

TL;DR

This paper addresses how vector-multiplet couplings in $N=2$ heterotic string vacua behave perturbatively. It shows that the tree-level prepotential is uniquely fixed by the dilaton’s Peccei-Quinn symmetry and by target-space dualities, while one-loop corrections are tightly constrained by exact discrete symmetries, yielding precise transformation laws for the perturbative prepotential and Wilsonian couplings. For toroidal compactifications of six-dimensional $N=1$ vacua, the authors derive explicit modular forms that determine the one-loop prepotential and gauge-threshold corrections, including a Green-Schwarz mixing term that couples the dilaton to torus moduli and a universal logarithmic threshold expressed through modular functions. The work also extends to moderately small Wilson-line deformations, providing a structured, symmetry-guided framework to compute higher-order moduli dependence in the one-loop prepotential and gauge couplings. Collectively, these results lay a foundation for understanding perturbative corrections and duality constraints in $N=2$ heterotic vacua, with implications for non-perturbative analyses and the role of dualities in effective actions.

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.