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String backgrounds of the form × ℳ where denotes 3-dimensional Minkowski space while ℳ is a 7-dimensional G -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 is replaced by AdS . 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., Journal of High Energy Physics, 2021 (5), ISSN:1126-6708, ISSN:1029-8479

String theory on AdS3 × S3 × S3 × S1 with pure NS-NS flux and minimal flux through one of the two S3’s is studied from a world-sheet perspective. It is shown that the spacetime spectrum, as well as the algebra of spectrum generating operators, matches precisely that of the symmetric orbifold of S3 × S1 in the large N limit. This gives strong support for the proposal that these two descriptions are exactly dual to one another., Journal of High Energy Physics, 2019 (6), ISSN:1126-6708, ISSN:1029-8479

The K3 sigma model based on the Z_2-orbifold of the D_4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra su(2)^6. By combining these different viewpoints we show that the N=(4,4) preserving symmetries of this theory are described by the discrete symmetry group Z_2^8:M_{20}. This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another., Comment: 55 pages

The K3 sigma model based on the Z2-orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra suˆ(2)6. By combining these different viewpoints we show that the N = (4, 4) preserving symmetries of this theory are described by the discrete symmetry group Z82 : M20. This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another., Journal of High Energy Physics, 2014, ISSN:1126-6708, ISSN:1029-8479

The perturbative spectrum of BPS-states in the E 8 × E 8 heterotic string theory compactified on T2 is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly using an auxiliary conformal field theory. The denominator formula of an extension Gext⊃G of this algebra is then found to appear in a certain heterotic one-loop N=4 topological string amplitude. Our construction thus gives an N=4 realisation of the idea envisioned by Harvey and Moore, namely that the ‘algebra of BPS-states’ controls the threshold corrections in the heterotic string., Journal of High Energy Physics, 2011 (6), ISSN:1126-6708, ISSN:1029-8479

The symmetries of string theory on AdS3×S3×T4 at the dual of the symmetric product orbifold point are described by a so-called Higher Spin Square (HSS). We show that the massive string spectrum in this background organises itself in terms of representations of this HSS, just as the matter in a conventional higher spin theory does so in terms of representations of the higher spin algebra. In particular, the entire untwisted sector of the orbifold can be viewed as the Fock space built out of the multiparticle states of a single representation of the HSS, the so-called ‘minimal’ representation. The states in the twisted sector can be described in terms of tensor products of a novel family of representations that are somewhat larger than the minimal one., Journal of High Energy Physics, 2016 (9), ISSN:1126-6708, ISSN:1029-8479