Electric/Magnetic Deformations of S^3 and AdS_3, and Geometric Cosets

TL;DR

The authors study asymmetric marginal deformations of SU(2)$_k$ and SL(2,$\mathbb{R}$)$_k$ WZW models, showing these yield exact heterotic string backgrounds with electric or magnetic fields that deform the target-space geometries into cosets like $S^2$ and $AdS_2$. By analyzing magnetic deformations of SU(2) and electric/hyperbolic and parabolic deformations of SL(2,$\mathbb{R}$), they derive explicit background fields, spectra, and modular-invariant partition functions, revealing a rich moduli space with well-defined limiting geometries (e.g., $\mathbb{R}\times S^2$, $AdS_2$, $H_2$) and connections to near-horizon black-hole geometries. The work shows how geometric cosets can arise as exact CFTs through asymmetric deformations, and discusses implications for holography and supersymmetry in $AdS_2\times S^2$ setups. Overall, it provides a unified CFT framework for exploring deformations of three-dimensional group manifolds into physically relevant, exact string backgrounds with potential holographic applications.

Abstract

We analyze asymmetric marginal deformations of SU(2)_k and SL(2,R)_k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu--Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S^3 or AdS_3, include in particular geometric cosets such as S^2, AdS_2 or H_2. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS_2 x S^2 background. We also comment on potential holographic applications.

Figures (1)

• Figure 1: We have summarized the various regimes appearing in magnetic/electric deformations of the $SU \left( 2\right)_k$ and $SL \left( 2, {\mathord{\mathbb R}} \right)_k$wzw models. Lighter bars indicate the signature, darker ones the sign of the curvature. Regions with $H^2<0$ have well-defined geometries with imaginary gauge field. Their string interpretation is therefore questionable.