There exists an intriguing relation between genus zero correlation functions in the H + 3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N +2g−2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program.

We propose holographic dualities between higher spin gravity theories extended with Chan-Paton factor on AdS 3 and a large N limit of two dimensional Grassmannian models with and without supersymmetry. These proposals are natural extensions of the duality without Chan-Paton factor, and the extensions are motivated by a higher dimensional version of the duality, which implies a possible relation to superstring theory via ABJ theory. As evidence for the proposals, we show that the free limit of the Grassmannian models have the higher spin symmetry expected from the dual gravity theory. Furthermore, we construct currents in the 't Hooft limit of the supersymmetric Grassmannian model and compare them with the currents from the bulk theory. One-loop partition function of the supergravity theory is reproduced by the 't Hooft limit of the Grassmannian model after decoupling a gauge sector.

We analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M ) symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as s = 2, 3, . . . , n, we evaluate the central charge c of the algebra and the level k of the affine currents with finite c, k. For the simplest case with n = 2, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing c, k from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for n = 2. We interpret the map of parameters by decomposing the algebra in the coset description.

We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces.

Gravity, itself a gauge theory of a spin 2 field, can be extended to a higher spin gauge theory on AdS spaces. Recently, Gaberdiel and Gopakumar conjectured that a large N limit of a 2d minimal model is dual to a bosonic subsector of a higher spin supergravity theory on 3d AdS space. We propose and test the untruncated supersymmetric version of this conjecture where the dual CFT is a large N limit of the N = 2 CP N Kazama-Suzuki model.Keywords: Higher spin gauge theory; AdS/CFT correspondence; W symmetry.PACS numbers: 11.25.Hf, 11.25.Tq BackgroundRecently, higher spin gravity theories have attracted a lot of attention due to their application to the AdS/CFT correspondence. Higher spin gravity theories extend ordinary gravity with gauge fields having spin s ≥ 3. On anti-de Sitter space, a higher spin gauge theory with an infinite number of spins and non-trivial interactions can be constructed, the so-called Vasiliev theory. In Ref. 1 it was proposed that a 4d Vasiliev theory is dual to the 3d O(N ) vector model. Very recently, a 3d Vasiliev theory was conjectured to be dual to a large N limit of a 2d minimal model.2 In Ref. 3, we have extended the conjecture to the case including supersymmetry. * The poster presentation was given by Y. Hikida.