A localising AdS${}_3$ sigma model

Abstract

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 $k_{\mathrm{s}}=1$ ($k=3$) 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 ${\mathrm{AdS}}_3$ backgrounds (at $k=3$).

34 pages + appendix; v2: added references

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Cited by in corpus (3)

• D-Branes in ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Non-supersymmetric strings on AdS${}_3$: a world-sheet perspective
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality