Fluxes in Heterotic and Type II String Compactifications

TL;DR

The paper investigates how turning on gauge and RR fluxes in heterotic on $K3\times \mathbb{T}^2$ and Type II on $K3$-fibraded Calabi–Yau spaces affects the established ${\cal N}=2$ duality. By mapping flux data through six-dimensional duality and comparing four-dimensional Green-Schwarz couplings, flux-induced superpotentials, and FI terms, it identifies a subset of fluxes with ${\mathbb P}^1_b$-support on the base that preserve the duality, while fluxes lacking this support resist simple dual interpretation. The work clarifies which flux configurations maintain dual descriptions and which lead to novel phenomena such as chirality, anomalies, and tachyonic instabilities, highlighting the roles of GS terms and the moduli-dependent superpotentials in determining vacuum structure. Overall, it sharpens the understanding of flux compactifications in the context of heterotic/type II duality and points to directions for extending dual descriptions beyond the ${\mathbb P}^1_b$-supported sector.

Abstract

In this paper we consider heterotic compactifications on K3 x T2 as well as type II compactifications on K3-fibred Calabi-Yau spaces with certain fluxes for the gauge and RR field strengths F and H turned on. By providing an identification of corresponding fluxes we show that the well-known N=2 heterotic/type II string-string duality still holds for a subset of all possible fluxes, namely those which arise from six-dimensional gauge fields with internal magnetic flux on the common two-sphere P1, which is the base space of the type II K3-fibration. On the other hand, F- and H-fluxes without P1-support, such as heterotic F-fluxes on the torus T2 or type II H-fluxes on cycles of the K3-fibre cannot be matched in any simple way, which is a challenge for heterotic/type II string-string duality. Our analysis is based on the comparison of terms in the effective low-energy heterotic and type II actions which are induced by the fluxes, such as the Green-Schwarz couplings related to flux-induced U(1) anomalies, the effective superpotential and the Fayet-Iliopoulos scalar potential.