Deformed Shatashvili-Vafa algebra for superstrings on AdS3 × ℳ7

Abstract

Abstract String backgrounds of the form 𝕄3× ℳ7 where 𝕄3 denotes 3-dimensional Minkowski space while ℳ7 is a 7-dimensional G2-manifold, are characterised by the property that the world-sheet theory has a Shatashvili-Vafa (SV) chiral algebra. We study the generalisation of this statement to backgrounds where the Minkowski factor 𝕄3 is replaced by AdS3. We argue that in this case the world-sheet theory is characterised by a certain $$ \mathcal{N} $$ N = 1 superconformal $$ \mathcal{W} $$ W -algebra that has the same spin spectrum as the SV algebra and also contains a tricritical Ising model $$ \mathcal{N} $$ N = 1 subalgebra. We determine the allowed representations of this $$ \mathcal{W} $$ W -algebra, and analyse to which extent the special features of the SV algebra survive this generalisation.