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The symmetric orbifold of 핋4 is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in AdS3 × S3 × 핋4. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the 2-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective. [ABSTRACT FROM AUTHOR]

Worldsheet string theory compactified on exceptional holomony manifolds is revisited following [1], where aspects of the chiral symmetry were described for the case where the compact space is a 7-dimensional G2-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret this result and extend it to Extra Twisted Connected Sum G2-manifolds, and to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of the latter construction lead us to conjecture new mirror maps. [ABSTRACT FROM AUTHOR]

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 = 1 superconformal W -algebra that has the same spin spectrum as the SV algebra and also contains a tricritical Ising model N = 1 subalgebra. We determine the allowed representations of this W -algebra, and analyse to which extent the special features of the SV algebra survive this generalisation. [ABSTRACT FROM AUTHOR]

Spectral flow, spacetime supersymmetry, topological twists, chiral primaries related to marginal deformations, mirror symmetry: these are important consequences of the worldsheet N = 2 superconformal symmetry of strings on Calabi-Yau manifolds. To various degrees of certainty, these features were also established when the target is either 7d or 8d with exceptional holonomy G2 or Spin(7) respectively. We show that these are more than mere analogies. We exhibit an underlying symmetry SW 3 2 2 making a bridge between the latter cases and K3 target spaces. Reviewing unitary representations of SW 3 2 2 leads us to speculate on further roles of this algebra in string theory compactifications and on the existence of topologically twisted versions of SW 3 2 2 theories. [ABSTRACT FROM AUTHOR]