Type IIA and Heterotic String Vacua in D=2

TL;DR

This paper investigates dualities between type IIA and heterotic string vacua compactified to two dimensions, deriving effective theories, analyzing flux-induced superpotentials, and connecting to known superpotentials in type IIB string theory.

Contribution

It establishes a duality between type IIA and heterotic string vacua in two dimensions and relates flux-induced superpotentials to those in type IIB compactifications.

Findings

Duality between type IIA and heterotic vacua confirmed at the effective theory level.

Superpotential generated by fluxes matches known superpotentials in specific cases.

Effective theories preserve four supercharges in two dimensions.

Abstract

We study type IIA string theory compactified on Calabi-Yau fourfolds and heterotic string theory compactified on Calabi-Yau threefolds times a two-torus. We derive the resulting effective theories which have two space-time dimensions and preserve four supercharges. The duality between such vacua is established at the level of the effective theory. For type IIA vacua with non-trivial Ramond-Ramond background fluxes a superpotential is generated. We show that for a specific choice of background fluxes and a fourfold which has the structure of a threefold fibred over a sphere the superpotential coincides with the superpotential recently proposed by Taylor and Vafa in compactifications of type IIB string theory on a threefold.