  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.
