Heterotic strings on homogeneous spaces

TL;DR

This work develops an exact, CFT-based framework for heterotic string backgrounds on homogeneous spaces formed as left cosets G/H with H a maximal torus. By combining asymmetric marginal deformations of WZW models with gauging techniques, the authors generate modular-invariant partition functions that describe backgrounds with NS-NS flux and gauge fluxes, and they demonstrate explicit constructions for SU(2)/U(1) and SU(3)/U(1)^2, including distinct Einstein structures on the flag space F3. The paper also extends the construction to general algebras via Kazama–Suzuki decompositions and abelian cosets, analyzes anomaly cancellation, and provides exact partition functions, highlighting the differences between Kähler and non-Kähler realizations. In addition, it introduces left-coset-based linear-dilaton backgrounds, yielding new supersymmetric vacua in six, four, three, and two dimensions with potential holographic and compactification applications. Overall, the work links geometric coset spaces with exact heterotic CFTs, offering versatile tools for flux vacua and controlled string backgrounds with reduced moduli.

Abstract

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU(2)/U(1) ~ S^2 (already described in a previous paper) and the SU(3)/U(1)^2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.

Figures (1)

• Figure 1: Root system for $\mathfrak{su}\left( 3\right)$.