Deformed Shatashvili-Vafa algebra for superstrings on AdS3 × ℳ7

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 N $$ \mathcal{N} $$ = 1 superconformal W $$ \mathcal{W} $$ -algebra that has the same spin spectrum as the SV algebra and also contains a tricritical Ising model N $$ \mathcal{N} $$ = 1 subalgebra. We determine the allowed representations of this W $$ \mathcal{W} $$ -algebra, and analyse to which extent the special features of the SV algebra survive this generalisation.

Abstract licence: CC BY

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