A localising AdS₃ sigma model

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