92 research outputs found

    Supersymmetric AdS3\mathrm{AdS}_3 supergravity backgrounds and holography

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    We analyse the conditions for AdS3Γ—M7\mathrm{AdS}_3 \times \mathcal{M}_7 backgrounds with pure NS-NS flux to be supersymmetric. We find that a necessary condition is that M7\mathcal{M}_7 is a U(1)\mathrm{U}(1)-fibration over a balanced manifold. We subsequently classify all N=(2,2)\mathcal{N}=(2,2) solutions where M7\mathcal{M}_7 satisfies the stronger condition of being a U(1)\mathrm{U}(1)-fibration over a Kahler manifold. We compute the BPS spectrum of all the backgrounds in this classification. We assign a natural dual CFT to the backgrounds and confirm that the BPS spectra agree, thus providing evidence in favour of the proposal.Comment: 39 pages; v2: minor corrections and references added; v3: section 2 shortened, final version as published in JHE

    String theory on AdS3\boldsymbol{\text{AdS}_{\mathbf{3}}} and the symmetric orbifold of Liouville theory

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    For string theory on AdS3_3 with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows us to show that the CFT dual of superstring theory on AdS3Γ—S3Γ—T4{\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4 for generic NS-NS flux is the symmetric orbifold of (N=4({\cal N}=4 Liouville theory)Γ—T4)\times \mathbb{T}^4. For the case of minimal flux (k=1k=1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T4\mathbb{T}^4, thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS3Γ—X{\rm AdS}_3 \times X.Comment: 33+10 page

    Strings on AdS3Γ—S3Γ—S3Γ—S1\text{AdS}_3 \times \text{S}^3 \times \text{S}^3 \times \text{S}^1

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    String theory on AdS3Γ—S3Γ—S3Γ—S1{\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1 with pure NS-NS flux and minimal flux through one of the two S3{\rm S}^3'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 S3Γ—S1{\rm S}^3\times \mathrm{S}^1 in the large NN limit. This gives strong support for the proposal that these two descriptions are exactly dual to one another.Comment: 25+23 page

    The Worldsheet Dual of the Symmetric Product CFT

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    Superstring theory on AdS3Γ—S3Γ—T4{\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4 with the smallest amount of NS-NS flux (`k=1k=1') is shown to be dual to the spacetime CFT given by the large NN limit of the free symmetric product orbifold SymN(T4)\mathrm{Sym}^N(\mathbb{T}^4). To define the worldsheet theory at k=1k=1, we employ the hybrid formalism in which the AdS3Γ—S3{\rm AdS}_3\times {\rm S}^3 part is described by the psu(1,1∣2)1\mathfrak{psu}(1,1|2)_1 WZW model (which is well defined). Unlike the case for kβ‰₯2k\geq2, it turns out that the string spectrum at k=1k=1 does {\it not} exhibit the long string continuum, and perfectly matches with the large NN limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.Comment: 29+24 page

    A holographic dual for string theory on AdS3Γ—S3Γ—S3Γ—S1\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1

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    The CFT dual of string theory on AdS3Γ—S3Γ—S3Γ—S1\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1 is conjectured to be the symmetric orbifold of the SΞΊ\mathcal{S}_\kappa theory, provided that one of the two Q5Β±Q_5^\pm quantum numbers is a multiple of the other. We determine the BPS spectrum of the symmetric orbifold in detail, and show that it reproduces precisely the BPS spectrum that was recently calculated in supergravity. We also determine the BPS spectrum of the world-sheet theory that is formulated in terms of WZW models, and show that, apart from some gaps (which are reminiscent of those that appear in the corresponding T4\mathbb{T}^4 calculation), it also reproduces this BPS spectrum. In fact, the matching seems to work as well as for the familiar T4\mathbb{T}^4 case, and thus our results give strong support for this proposal.Comment: 41 pages, 2 figure

    Higher spin algebras and large N=4\mathcal{N}=4 holography

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    A new family of higher spin algebras that arises upon restricting matrix extensions of shs[Ξ»]\mathfrak{shs}[\lambda] is found. We identify coset CFTs realising these symmetry algebras, and thus propose new higher spin-CFT dual pairs. These higher spin theories arise naturally as a subsector of string theory on AdS3Γ—S3Γ—S3Γ—S1{\rm AdS}_3\times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1 for specific ratios of the radii of the two spheres.Comment: 22 page

    Holographic Weyl anomaly in string theory

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    We compute the worldsheet sphere partition function of string theory on global AdS3_3 with pure NS-NS flux. Because of an unfixed M\"obius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unambiguous. We show that it precisely reproduces the holographic Weyl anomaly and the ambiguous terms correspond to the possible counterterms of the boundary CFT.Comment: 9 pages + appendi
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