A localising AdS₃ sigma model

We construct a CFT with sl(2,R)_k 𝔰𝔩(2,ℝ)k symmetry at the ‘tensionless’ point k=3 k=3 , which is distinct from the usual SL(2,R)ₖ₌₃ SL(2,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 kₛ=1 ( k=3 k=3 ) can be constructed by replacing the AdS_3 AdS3 factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of AdS_3 × S^3 × T^4 AdS3×S3×𝕋4 , as well as the recently discussed example of AdS_3 × S^3 × S^3 × S^1 AdS3×S3×S3×S1 . However, our analysis does not require supersymmetry and also applies to bosonic { AdS}_3 backgrounds (at k=3 k=3 ).