Deformed Shatashvili-Vafa algebra for superstrings on AdS3 \xd7 \u21337

Abstract

String backgrounds of the form \U0001d5443× ℳ7 where \U0001d5443 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 \U0001d5443 is replaced by AdS3. We argue that in this case the world-sheet theory is characterised by a certain mathcal{N} = 1 superconformal mathcal{W} -algebra that has the same spin spectrum as the SV algebra and also contains a tricritical Ising model mathcal{N} = 1 subalgebra. We determine the allowed representations of this mathcal{W} -algebra, and analyse to which extent the special features of the SV algebra survive this generalisation.