We construct a CFT with $\mathfrak{ sl}(2,\mathbb{ R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{ SL}(2,\mathbb{ R})_{ k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{ \rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{ AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{ AdS}_3 \times \mathrm{ S}^3 \times \mathbb{ T}^4$, as well as the recently discussed example of $\mathrm{ AdS}_3 \times \mathrm{ S}^3 \times \mathrm{ S}^3 \times \mathrm{ S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${ \rm AdS}_3$ backgrounds (at $k=3$).
Categories: hep-th